Chapters 1-2

Question 1

Are differentiability and continuity the same?

Answer 1

no (sharp corners that are continuous, , square root functions that have ENDPOINTS (endpoints cannot be differentiated)

Question 2

The domain of the derivative function is AT MOST…

Answer 2

the domain of the original function

Question 3

What are the three things you MUST SHOW at EVERY continuity/discontinuity question?

Answer 3

what f(number) =
what the limits from left and right side =
what the limit equals (should be covered by previous step)

Question 4

When is f(x) used in a continuity/discontinuity limit problem?

Answer 4

When, and only when, you are plugging in actual values for x and y and stuff to solve for a value

Question 5

Define secant line and how to find it…

Answer 5

the “rate of change,” UNF

Question 6

List out the general steps to solving a related rates problem…

Answer 6

1. determine (through visualization with shapes, info in the question, etc.) the direction and magnitude of given measures and rates of change
2. determine the equation relevant to the question
3. solve for the unknown
4. Write a FULL SENTENCE ANSWER clarifying the meaning of the found value

Question 7

How do you solve an infinite limit?

Answer 7

multiply everything by the fraction version of the highest SHARED (numerator AND denominator have this) degree so that everything extra is over infinity, and thus 0

if the numerator and denominator have the same degree, divide numerator by denominator

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