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**MATH 260 DeVry Week 4 Discussion Latest**

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**MATH 260 DeVry Week 4 Discussion Latest**

**MATH 260 DeVry Week 4 Discussion**

__Trigonometric Functions (graded)__

Trigonometric functions are some of the most important functions that you will explore. Remember that they are periodic, so they have many real-world applications in studying various kinds of waves and frequencies. Here are some questions that we will address. Please post answers in this thread.

- What are the formulas for the derivatives of the trig functions?
- How do we use them to find derivatives of more complex functions involving trig forms?
- How can we use the trig identities to rewrite functions so that we can apply the basic formulas?
- What are real-world applications for trig functions, particularly those that come from your program?
- Explain how you can use the derivative to explore these applications.

Please feel free to use examples from the homework to illustrate your answers.

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**MATH 260 DeVry Week 3 Quiz Latest**

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**MATH 260 DeVry Week 3 Quiz Latest**

**Math 260 DeVry Week 3 Quiz**

**Question 1. Question : (TCO 2)** Find all of the derivatives:

y = -3×3 + 2×2 – 9x + 2?x + 13 -9x^2+4x-9+2pi -18x+4 -18 0

Instructor Explanation: See Chapter 23.9, Week 2 Lecture

y’ = -9×2 + 4x – 9 + 2?, y” = -18x + 4, y”’ = -18, y(4) = 0

**Question 2. Question : (TCO 2)** Choose the letter of the correct Chain Rule for

f(x), g(x), h(x)

are continuous functions of x.

**Question 3. Question : (TCO 2)** Find y’ for y = (x2 – 3)(2×2 – 1),

use the product rule and simplify your answer.

**Question 4. Question : (TCO 2)** Find f ‘(-2) for

**Question 5. Question : (TCO 2)** Find v(t) and a(t) for s(t) = 2(3t2 + 1)2, then find the velocity and acceleration at 1 second.

**Question 6. Question : (TCO 2)** Find the expression for the slope of the tangent line for .

Then find the slope of the tangent line at x = 1.

What is the slope of the curve, f(x),

at x = 1?

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**MATH 260 DeVry Week 3 Discussion Latest**

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**MATH 260 DeVry Week 3 Discussion**

__Curve Sketching (graded)__

Given the function: f(x) = 5×3 – 125x

Take turns determining the following.

- Domain and Range;
- X and Y Intercepts;
- Maxima and Minima;
- Increasing/Decreasing Behavior;
- Concavity; and
- Point(s) of inflection.

Be sure that you explain how you determined each part.

Also, if you have other questions that you would like me to address, post them here.

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**MATH 260 DeVry Week 2 Quiz Latest**

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**MATH 260 DeVry Week 2 Quiz Latest**

**Math 260 DeVry Week 2 Quiz**

**Question 1. Question: (TCO 1)** If: then which of the following must be true? f(x) is discontinuous at x = c f(x) is continuous at x = c f(x) has a removable discontinuity at x = c f(x) = f(c)

**Question 2. Question: (TCO 1)** Find

**Question 3. Question: (TCO 1)** Determine the following limit from the table below:

x 8.9 8.99 8.999 8.9999 8.99999

f(x) -0.02 -0.007 -0.0002 -0.00007 -0.000002 -0.000002

**Question 4. Question: (TCO1)** Find the following limit:

.

0

1

Undefined

**Question 5. Question: (TCO1)** At time = 0, a diver jumps from a diving board that is 20 feet above the water.

The position of the diver is given by s(t) = -16t2 + 20, s in feet, t in seconds.

Give the expression for the instantaneous velocity of the diver at any point on her path, then find the velocity at .3 seconds.

**Question 6. Question: (TCO 1)** Find the average rate of change of y with respect to x from P to Q. Then find the instantaneous rate of change (velocity) of y with respect to x at P. (x in seconds, y in meters)

y = 2×2 + 1, P(-2, 9), Q(2.1, 9.82)

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**MATH 260 DeVry Week 2 Discussion**

__A Deeper Understanding of Derivatives (graded)__

This week, we will be exploring the concept of derivative. Here are some questions that we will address. Please post your answers in this thread.

- What is the derivative? Mathematically and/or real world?
- What is the power rule and how do we use it to find a derivative?
- What is the product rule and how do we use it to find a derivative?
- What is the quotient rule and how do we use it to find a derivative?
- What is the chain rule and how do we use it to find a derivative?
- What information can be obtained from derivatives?
- Please provide an example from the real world and explain the information that you could gain from it.
- How do we find higher-order derivatives?
- How are the higher-order derivatives for f(x) = 3×6 different from the higher-order derivatives of f(x) = 2x-4?

Please use examples from the homework to illustrate your answers.

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**MATH 260 DeVry Week 1 iLab 1**

**MATH260**

**MATH 260 DeVry Week 1 iLab 1**

**MATH 260 DeVry Week 1 iLab 1**

**Part I – Limits**

The limit of a function is a way to see the value that the function approaches as a variable in that function gets close to but not necessarily equal to some other value The four ways we have looked at to find the limit of a function are:

direct substitution of the limiting number into the function ‚

simplifying the function first then substitute (factor or rationalize)

ƒ examine values of the function from the left and right of the limiting number „

examine the graph of the function at the limiting value

**Category 1:** Directions: Look at the examples below then answer question 1 & 2.

1.) Which of the Rules or Processes,‚,ƒ,„ mentioned aboveis/are being used to find the limit in the Category 1 examples above ?

2.) For the following limit why can you not use the same process as the examples above ?

**Category 2:** Directions: Look at the examples below then answer question 3 & 4.

3.) Which of the Rules or Processes,‚,ƒ,„ mentioned aboveis/are being used to find the limit in the Category 2 examples above ?

4.) If you graph a Category 2 problem, what feature will appear at the limiting value ?

**Category 3:** Directions: Look at the examples below then answer question 5.

5.) Which of the Rules or Processes,‚,ƒ,„ mentioned above is/are being used to find the limit in the Category 3 examples above ?

**Category 4:** Directions: Look at the examples below then answer question 6 & 7.

6.) What method/rules are used to find the limit when xà∞ ?

7.) Use the rules for finding a limit as x approaches infinity to find each limit a-c.

a.) = b.) = c.) =

The Limit from the left, the limit from the right:

Left and Right hand limits and the General limit.

To find a left hand limit means to find the limit as the limiting number is approached only from the left of the limiting number.

To find a right hand limit means to find the limit as the limiting number is approached only from the right of the limiting number.

The limit of a function can be different from the left than it is from the right. But if the limit from the left equals the same value as the limit from the right, then the general limit exists and is that value.

8.) Using the table below, answer the questions about

x -.01 – .001 -.0001 .01 .001 .0001

f(x) 2.1 2.0001 2.0000001 .9 .9999 .9999999

**Part II:**

__(a) Piecewise functions__

__(b) discontinuities__

**(a) A piecewise function** is defined using two or more equations each with a specific domain. Each equation gives a part of the graph based on your choice of x.

**(b) A function is considered to be discontinuous** at a point, a, if any of the following are true:

1.) f(c) is undefined

2.) any small change in x (a move to the left or right on the x-axis) produces a “large” change in f(x)

3.) does not exist or is undefined.

A discontinuity at x = a is removable if exists.

Given the following piecewise function and it’s graph below answer questions 9 – 16.

9.) For x = -2, What is the right hand limit ?

10.) Does exist ? Why or Why Not ? If so, find

11.) Does this function have a discontinuity at x = -2 ? If so, name the reason why. Is it a removable discontinuity ? Why or why not

12.)

13.) =

14.) What feature can be found in the graph at x = 4 ?

15.) for x > 4 , find

16.) Using interval notation describe where this graph is continuous.

17.) Is it possible for a function to have a limit from the left be infinite and the limit from the right be zero if both limits are approaching the same number ? Sketch a graph if possible.

18.) Considering that discontinuities occur at holes, jumps, and vertical asymptotes. Is it possible for a function to have a limit from the left of∞and the limit from the right -∞ if the number that is being approached is NOT the location of a vertical asymptote ? Explain.

**Part III:**

**Derivatives:**** **gives us the rate of change of what a function is modelling. If the function is describing the position of a moving object, the derivative can tell us more about how the object is moving, like the velocity or acceleration of the object.

**An application of the derivative: Position and Velocity**

The position function is a measure of location of an object along a path of travel with respect to time. As the object moves along its path, it goes through many changes as time elapses like changes in position and velocity. Velocity is a measure of how fast and can also indicate if the object is speeding up, slowing down, or at a constant.

**Velocity** has two measures, average velocity and instantaneous velocity.

To find Average velocity use the position function, s(t), and a time period t1 to t2. Average velocity is the change in position over a period of time. , t1 < t2

Instantaneous velocity is how fast a particle is going at a particular instant in time. To find it, you must use the first derivative of the position function. v(t) = ,note: h is the same as?x

The Acceleration is found by taking the derivative of the velocity function. a(t) =

19.) Given that a moving object’s path follows the function

a.) Use the definition v(t) = to find the expression for the Velocity of the object where the initial velocity is 50 ft/sec and the initial height is 600ft. Show all work.

b.) Find the average velocity of the object between t = 1 and t = 3 seconds. c.) Find the instantaneous velocity of the object at t = 2 seconds

**A graph and its derivative in general:**

For any curve f(x), f ’(x) gives the rate of change of the y’s with respect to the x’s on the graph of the function, also known as the slope of the curve.

Like a straight line, a curve has a positive slope if it is going uphill and a negative slope if it is going downhill (from left to right on the Cartesian Plane).

20.) Plot the function and it’s derivative in your graphing calculator. Look carefully at the two graphs: How does the graph of f’(x) reflect the changes in the slope of the graph of the curve f(x) ?

21.) In a parallel circuit, current moves through multiple paths. That means two resistors that are wired in parallel circuits havea lower total resistance than either of the parallel resistors.

.wikimedia.org/wiki/File:Resistorsparallel.png”>

So, if you know what the smaller resistor is, then as the other resistor gets larger, the total resistance will never be larger than the smallest resistance in the circuit. It has a limit.

The formula for resulting resistance, RT, (the combined resistance) of two resistors in a parallel circuit,

one R1 and the other R2 is .

a.) If R1 is 10 Ω, find the limit of RT as R2à ∞.

b.) Find RT for R1 = 10 and R2 = 5

c.) Find RT for R1 = 10 and R2 = 250

d.) Given b.) and c.) above, will RT ever go above 10 ? Explain why.

22.) Give the formula for the slope of a straight line and then the formula for the slope of a curve.

How are the formulas the alike? How are they different?

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**MATH 260 DeVry Week 1 Discussion Latest**

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**MATH 260 DeVry Week 1 Discussion Latest**

**MATH 260 DeVry Week 1 Discussion**

__Understanding Limits and Derivatives (graded)__

This week, we will be dealing with limits and their connection to the derivative. Here are some questions that we will address. Please post your answers in this thread.

- What is a limit?
- How is the mathematical meaning of a limit similar to and different from how we perceive a limit in the real world?
- How do we find a limit?
- Under what circumstances is a limit undefined?
- How does continuity play a role in finding limits and vice versa?
- Discuss the continuity of the following: f(x) = (x + 3)/(x^2 – 9).
- How do limits play a role in exploring vertical and horizontal asymptotes?
- How are one-sided and two-sided limits related? How can the relation sometimes be used to determine the existence or nonexistence of a limit?
- How can the answers to these questions help us link the concept of limit to the concept of derivative?
- What is the limit definition of derivative? How can we use it to find a derivative?

Please feel free to use examples from the homework to illustrate your answers.

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**MATH 221 DeVry Week 1 Discussion Latest**

There are lots of “helps” available in this course. Please find one and tell us why it will be useful for you.

Then give careful directions for how to find that “help.”

Be sure to look in the left hand navigation area and also on the upper toolbar as well as in MSL.

Try to find one which hasn’t already been mentioned.

**MATH 221 DeVry Week 2 Discussion Latest**

A regression equation can be graphed. The graph will go uphill as we look at it going from the left to the right; or it will go downhill as we look at it going from the left to the right; or it will be parallel to the x-axis.

Take a look at several examples in the text or in the Homework and ponder for a while.

Then write a very short idea about what’s going on with correlation (consider the r-value), with slope, and anything else you might notice.

Rather than being redundant, please read the ideas your classmates post and comment or add to what they observed.

**MATH 221 DeVry Week 3 Discussion Latest**

__Probability and Odds (graded)__

Please watch for a new question each day. Please post 3 times minimum.

And be sure to follow the post on 3 different days requirement as well as the 1st post before midnight Wednesday requirement

**MATH 221 DeVry Week 4 Discussion Latest**

__Discrete Probability Variables (graded)__

There will be a new question each day. Be sure to post on 3 different days.

If I can count it, then it’s discrete. If I can measure it, then it’s continuous.

Please keep these 2 statements in mind as we study random variables.

For today’s post please give an example of a discrete random variable.

- If I have 8 cans of coca cola in my refrigerator, that’s a discrete random variable — I can count them. But, if I say that I have 12 ounces in each can, that’s continuous because that’s a measurement. And I can’t really say that it’s 12 ounces. It might be 12. 1 or 11.9 or it could even be 12.05 or 11.95. Getting more accurate it could be 12.00001 or 11.99999. And that’s why we call it continuous — on the number line I can always get a little closer than I was a moment ago.

**MATH 221 DeVry Week 5 Discussion Latest**

__Interpreting Normal Distributions (graded)__

Please look for a new question each day. Please post on 3 different days.

A skill which will be tremendously important in the coming weeks is sketching a normal curve. And to sketch it we need to draw the x-axis accurately.

Here’s one for a curve when the mean is 0 and the standard deviation is 1.

_____-3_____-2_____-1_____*0*_____+1_____+2_____+3_____

And here’s one for a curve when the mean is 40 and the standard deviation is 4.

_____28_____32_____36____*40*____44_____48_____52_____

And here’s another for a curve when the mean is 10 and the standard deviation is 6.

_____-8_____-2_____+4_____*10*_____16_____22_____28_____

For today’s post please find a normal distribution in the text or in MSL and sketch the appropriate x-axis.

**MATH 221 DeVry Week 6 Discussion Latest**

__Confidence Interval Concepts (graded)__

Please watch for a new question each day. Be sure to post on 3 different days.

There are many online calculators for confidence intervals.

Find one. Use it. Compare your answer with an answer from one of the examples in the book (that way you’ll know if it is correct). Then share the URL with us and talk about how easy or hard it is to use.

**MATH 221 DeVry Week 7 Discussion Latest**

__Rejection Region (graded)__

Please watch for a new question each day. Be sure to post on 3 different days.

How is the rejection region defined, and how is that related to the p value?

**MATH 221 DeVry Complete Week Discussions Package**

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**MATH 221 DeVry Week 1 Discussion Latest**

There are lots of “helps” available in this course. Please find one and tell us why it will be useful for you.

Then give careful directions for how to find that “help.”

Be sure to look in the left hand navigation area and also on the upper toolbar as well as in MSL.

Try to find one which hasn’t already been mentioned.

**MATH 221 DeVry Week 2 Discussion Latest**

A regression equation can be graphed. The graph will go uphill as we look at it going from the left to the right; or it will go downhill as we look at it going from the left to the right; or it will be parallel to the x-axis.

Take a look at several examples in the text or in the Homework and ponder for a while.

Then write a very short idea about what’s going on with correlation (consider the r-value), with slope, and anything else you might notice.

Rather than being redundant, please read the ideas your classmates post and comment or add to what they observed.

**MATH 221 DeVry Week 3 Discussion Latest**

__Probability and Odds (graded)__

Please watch for a new question each day. Please post 3 times minimum.

And be sure to follow the post on 3 different days requirement as well as the 1st post before midnight Wednesday requirement

**MATH 221 DeVry Week 4 Discussion Latest**

__Discrete Probability Variables (graded)__

There will be a new question each day. Be sure to post on 3 different days.

If I can count it, then it’s discrete. If I can measure it, then it’s continuous.

Please keep these 2 statements in mind as we study random variables.

For today’s post please give an example of a discrete random variable.

- If I have 8 cans of coca cola in my refrigerator, that’s a discrete random variable — I can count them. But, if I say that I have 12 ounces in each can, that’s continuous because that’s a measurement. And I can’t really say that it’s 12 ounces. It might be 12. 1 or 11.9 or it could even be 12.05 or 11.95. Getting more accurate it could be 12.00001 or 11.99999. And that’s why we call it continuous — on the number line I can always get a little closer than I was a moment ago.

**MATH 221 DeVry Week 5 Discussion Latest**

__Interpreting Normal Distributions (graded)__

Please look for a new question each day. Please post on 3 different days.

A skill which will be tremendously important in the coming weeks is sketching a normal curve. And to sketch it we need to draw the x-axis accurately.

Here’s one for a curve when the mean is 0 and the standard deviation is 1.

_____-3_____-2_____-1_____*0*_____+1_____+2_____+3_____

And here’s one for a curve when the mean is 40 and the standard deviation is 4.

_____28_____32_____36____*40*____44_____48_____52_____

And here’s another for a curve when the mean is 10 and the standard deviation is 6.

_____-8_____-2_____+4_____*10*_____16_____22_____28_____

For today’s post please find a normal distribution in the text or in MSL and sketch the appropriate x-axis.

**MATH 221 DeVry Week 6 Discussion Latest**

__Confidence Interval Concepts (graded)__

Please watch for a new question each day. Be sure to post on 3 different days.

There are many online calculators for confidence intervals.

Find one. Use it. Compare your answer with an answer from one of the examples in the book (that way you’ll know if it is correct). Then share the URL with us and talk about how easy or hard it is to use.

**MATH 221 DeVry Week 7 Discussion Latest**

__Rejection Region (graded)__

Please watch for a new question each day. Be sure to post on 3 different days.

How is the rejection region defined, and how is that related to the p value?

Downloading is very simple, you can download this Course here:

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**MATH 221 DeVry Complete Week Discussions Package**

**MATH221**

**MATH 221 DeVry Complete Week Discussions Package**

**MATH 221 DeVry Week 1 Discussion Latest**

There are lots of “helps” available in this course. Please find one and tell us why it will be useful for you.

Then give careful directions for how to find that “help.”

Be sure to look in the left hand navigation area and also on the upper toolbar as well as in MSL.

Try to find one which hasn’t already been mentioned.

**MATH 221 DeVry Week 2 Discussion Latest**

A regression equation can be graphed. The graph will go uphill as we look at it going from the left to the right; or it will go downhill as we look at it going from the left to the right; or it will be parallel to the x-axis.

Take a look at several examples in the text or in the Homework and ponder for a while.

Then write a very short idea about what’s going on with correlation (consider the r-value), with slope, and anything else you might notice.

Rather than being redundant, please read the ideas your classmates post and comment or add to what they observed.

**MATH 221 DeVry Week 3 Discussion Latest**

__Probability and Odds (graded)__

Please watch for a new question each day. Please post 3 times minimum.

And be sure to follow the post on 3 different days requirement as well as the 1st post before midnight Wednesday requirement

**MATH 221 DeVry Week 4 Discussion Latest**

__Discrete Probability Variables (graded)__

There will be a new question each day. Be sure to post on 3 different days.

If I can count it, then it’s discrete. If I can measure it, then it’s continuous.

Please keep these 2 statements in mind as we study random variables.

For today’s post please give an example of a discrete random variable.

- If I have 8 cans of coca cola in my refrigerator, that’s a discrete random variable — I can count them. But, if I say that I have 12 ounces in each can, that’s continuous because that’s a measurement. And I can’t really say that it’s 12 ounces. It might be 12. 1 or 11.9 or it could even be 12.05 or 11.95. Getting more accurate it could be 12.00001 or 11.99999. And that’s why we call it continuous — on the number line I can always get a little closer than I was a moment ago.

**MATH 221 DeVry Week 5 Discussion Latest**

__Interpreting Normal Distributions (graded)__

Please look for a new question each day. Please post on 3 different days.

A skill which will be tremendously important in the coming weeks is sketching a normal curve. And to sketch it we need to draw the x-axis accurately.

Here’s one for a curve when the mean is 0 and the standard deviation is 1.

_____-3_____-2_____-1_____*0*_____+1_____+2_____+3_____

And here’s one for a curve when the mean is 40 and the standard deviation is 4.

_____28_____32_____36____*40*____44_____48_____52_____

And here’s another for a curve when the mean is 10 and the standard deviation is 6.

_____-8_____-2_____+4_____*10*_____16_____22_____28_____

For today’s post please find a normal distribution in the text or in MSL and sketch the appropriate x-axis.

**MATH 221 DeVry Week 6 Discussion Latest**

__Confidence Interval Concepts (graded)__

Please watch for a new question each day. Be sure to post on 3 different days.

There are many online calculators for confidence intervals.

Find one. Use it. Compare your answer with an answer from one of the examples in the book (that way you’ll know if it is correct). Then share the URL with us and talk about how easy or hard it is to use.

**MATH 221 DeVry Week 7 Discussion Latest**

__Rejection Region (graded)__

Please watch for a new question each day. Be sure to post on 3 different days.

How is the rejection region defined, and how is that related to the p value?

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**MATH 062 DeVry Week 7 Discussion**

**MATH062**

**MATH 062 DeVry Week 7 Discussion**

**MATH 062 DeVry Week 7 Discussion**

__Problem Solving and Success Strategies (graded)__

How do you prepare for a post-test? What is the learning strategy that you use? In the homework, you can rely heavily on the view an example and the help me solve this features. Do those help you learn the material well enough to be successful on the post-test? Do you spend a lot of time with the course or publisher videos? Is the extra practice the most helpful? What strategy have you found so far that works, and is there anything that you would recommend someone new to this course avoid doing or relying solely upon?

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**MATH 062 DeVry Week 6 Discussion**

**MATH062**

**MATH 062 DeVry Week 6 Discussion**

**MATH 062 DeVry Week 6 Discussion**

__Exponents and Polynomials in the Real World (graded)__

Have you ever seen a semi-truck with a curved truck bed rather than a flat one? Why are most lenses curved? These are just a few examples in which we have real-world examples that make use of exponents and polynomials. Research common applications of exponents (don’t limit yourself to physics; check business, finance, and the medical world for examples, as well), and post what you find here. You may also post explanations of vocabulary found in this section, and explain why it is important. Be sure your posts are unique and not just repetitions of what someone else has already submitted.

]]>