Chapter 1

Question 1

(x→0)lim(sinx/x)

Answer 1

1

Question 2

(x→0)lim((1-cosx)/x))

Answer 2

0

Question 3

T or F: ∞/∞ is a valid answer

Answer 3

F; that’s called indeterminate form

Question 4

terms for “No Answer” for functions & limits

Answer 4

Undefined for functions; DNE for limits

Question 5

how to find VA

Answer 5

literally just set x equal to whatever number will render the function undefined (which is usually 0, for stuff like ln, and when it’s an expression in the denominator)

Question 6

3 steps to guaranteeing c can be found w/ Intermediate Value Theorem

Answer 6

1) Sketch the graph within the interval
2) see if f(intvl val to left) and f(intvl val to right) exist and surround the value of c (which is prob 0)
3) Declare whether IVT can be used, and use trace to find c on that interval

Question 7

what equation do you need to remember when finding the derivative

Answer 7

f¹(x) = (h→0)lim(f(x+h) - f(x))/h

Question 8

2 steps to find tangent line if you have derivative & point of tangency

Answer 8

1) plug the x-val of the given point into derivative to get the slope of the tangent line
2) use y - y1 = m(x - x1) to get the tan line equation by plugging in the newly found slope & coordinates of the given point; simplify to get the line

Question 9

how to get 1 from sin & cos

Answer 9

1 = sin² + cos²

Question 10

how to get tan from sin & cos

Answer 10

tan = sin/cos

Question 11

sin2θ

Answer 11

2sincos

Question 12

cos2θ with sin & cos

Answer 12

cos² - sin²

Question 13

cos2θ with sin

Answer 13

1 - 2sin²

Question 14

cos2θ with cos

Answer 14

2cos² - 1

Question 15

what are you looking for when solving limits where x reaches positive/negative infinity

Answer 15

horizontal asymptotes

Question 16

HA when n deg > d deg

Answer 16

NA

Question 17

HA when n deg < d deg

Answer 17

0

Question 18

when x reaches negative infinity for a limit, what is the sqrt(9x²)?

Answer 18

-3x

Question 19

3 steps to find continuity

Answer 19

1) Is f(x) defined?
2) Is the limit that f(x) when n -> x defined?
3) Do those values equal each other?

If all 3 are right then it’s continuous

Question 20

How to find if a discontinuity is removable or not thru a limit

Answer 20

Take the limit at x reaching the discontinuity:

• Get # back: removable
• Get DNE back: non-removable

Question 21

How to find if a discontinuity is removable or not thru a graph

Answer 21

• Holes are removable

- Breaks/VA’s are not

Question 22

How to make function continuous (really just 1 step)

Answer 22

1) Make a limit a little less than the number that breaks the piecewise function, and a limit a little more
2) Set them equal to each other and solve

Question 23

What is the derivative for purposes to answer that dang question 15

Answer 23

if x in f’(x) is the x-val of the point of tangency, then plugging it in to the derivative equation gives the slope needed to touch this point in the line of tangency.

If you need the y-coord for the point of tangency, take the x-tan-coord & plug into original f(x) that the derivative came from