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Give brief but clear answers to the questions below. Click on this link to send me an email with your answers. Make sure to type 'Calculus Assignment' and the date in the subject line.

For Friday, April 2

1. How do the techniques in this chapter `reverse' the process of differentiation we've learned to date?
2. What are the two types of differential equations mentioned in the section? How are they different?
3. Which function is its own derivative? How are trig functions related to their higher derivatives?

For Monday, April 5

1. How does our interpretation of the derivative as a rate help us to express mathematically the exercises on page 51?
2. Write a rate question similar to those on page 51, that is, some question that gives information about the rate of a phenomenon.

For Wednesday, April 7

1. What sorts of functions have horizontal asymptotes? What sorts of functions have vertical asymptotes?
2. What do we actually mean when we say 'The limit as x approaches c of f(x) is infinity'?
3. Recall what a rational function is from section 1.2. When does a rational function have a horizontal asymptote? When does a function have a horizontal asymptote that is not y=0?

For Friday, April 9

1. Give a verbal explanation of how L'Hopitals rule is used to evaluate limits. Be careful to say what form the function must be in to apply the rule.
2. How can we use L'Hopitals rule to evaluate limits?
3. Find another word that uses a circumflex in its spelling. :)

For Monday, April 12

1. Compare the Mean Value Theorem to the Intermediate Value Theorem. How can we interpret the MVT in terms of slopes?
2. Explain the connection between Rolle's Theorem and the Mean Value Theorem. Go into greater detail than the section.
3. If two functions have the same derivative, must they be equal? If they are not equal, how are they related?

For Wednesday, April 14

1. We know that the first derivative of a function measures its slope. What does the second derivative measure?
2. What is an inflection point?
3. If the college says that 'Tuition is going up only 3% this year, which is the third straight year that the increase in tuition has gone down,' then what shape is the graph of tuition with respect to time?

For Friday, April 16

For Monday, April 19

1. How are velocity, acceleration, and jerk all related?
2. What process lets us find a function given its derivative? Where have we seen this before?
3. What is the velocity of a projectile when it reaches its maximum height? Why is this the case?

For Wednesday, April 21

For Friday, April 23

1. Study hard and get plenty of rest the night before.
2. PLEASE come talk to me in advance about any topics that you're having trouble with.

For Monday, April 26

1. (You'll need a graphing utility or a creative imagination for this first exercise.) If we zoom in really close to a point on a continuous and differentiable function, what does the graph look like? What equation (other than the function itself) describes what we see?
2. Why might it be useful to approximate a function with polynomials?
3. How do polynomial approximations explain how your calculator is able to figure out something like sin(2.573) in under a second?

For Wednesday, April 28

1. What is the purpose of Newton's Method?
2. What does the word iterative mean and how does it apply to Newton's Method?
3. What happens if, at some point during the interation of Newton's Method, you get that x _n+I = x _n ? (Hint: Look at the formula used in the iteration.

For Friday, April 30

1. What technique allows us to find slopes of curves that are not functions of one variable?
2. Why is implicit differentiation an extension of the chain rule.
3. We have seen implicit differentiation twice before in this course, namely to find derivatives of two types of functions. Which two types?

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