Chapter 2 Test

Question 1

Steps to finding the limit

Answer 1

Plug in
Simplify
Then plug bigger and smaller numbers in

Question 2

The limit is infinity when…

Answer 2

A small number is over a huge, exponential number
The function has a vertical asymptote (x-# in the denom)
The func is exponential

Question 3

Jump function

Answer 3

The numbers in a piecewise approach the same limit but are different
Limit DNE

Question 4

How to tell when the function approaches the limit at different spots

Answer 4

Left hand and right hand limits
Plug in numbers bigger and smaller than the limit
If they match, the limit exists and its the given number

Question 5

The limit does not exist when

Answer 5

Right hand limit does not match left hand limit
Function is sin or cosine
If it jumps

Question 6

When you see an absolute value…

Answer 6

Plug in pos and neg numbers

Question 7

When limit approaches infinity…

Answer 7

Degrees of leading coefficients
n<d -> 0
n=m -> ratio of leading coefficients
n>d infinity or negative infinity

Question 8

Limit with infinity with VA in bottom

Answer 8

Approach a from the left and right, will either be neg or pos infinity or DNE if they don’t match
1/x; x=0 lim DNE
1/x^2 x=0 lim pos infinity

Question 9

Sin x/x=

Answer 9

1

Question 10

The limit exists as long as (GRAPH)…

Answer 10

The limit has a line of the left and right, doesn’t matter if there is a hole

Question 11

The limit doesn’t exist if (GRAPH)…

Answer 11

The limit doesn’t match on the left and right

Question 12

The graph is continuous if…

Answer 12

There’s no holes
There’s lines on the left and right
No jumps

Question 13

Horizontal asymptotes

Answer 13

n<d, y=0
n=d, L.C of n/L.C of d
n>d, none

Question 14

How do you find EBM

Answer 14

Subtract the powers and keep the numbers in front the same

Question 15

How do you find left and right EBM

Answer 15

Which ever grows quicker on the left and right.

Question 16

Tangent line

Answer 16

Find the IROC
Find x, f(x)
Plug into point slope

Question 17

Normal line

Answer 17

Find the tangent
Find the negative reciprocal of the tangent
Use the same points
Use point slope

Question 18

How do you find the average R.O.C

Answer 18

Plug in x1 and x2 to get y1 +y2
x2-x1/y2-y1

Question 19

Instant R.O.C

Answer 19

Use f(x+h) - f(x)/h
Plug in x to to x+h and f(x)

Question 20

How do you find the secant line

Answer 20

Plug in given x’s to the equation
Find slope
Plug into point slope

Question 21

Left hand and right hand limit of a piecewise

Answer 21

Find the one that is the smallest, plug in numbers smaller
Find the one that is the biggest
plug in numbers bigger
If they are equal, the lim exists