Test 1

Question 1

even degree and positive leading coefficient

Answer 1

lim as x –> inf –> inf

lim as x–> -inf –> inf

Question 2

even degree and negative leading coefficient

Answer 2

lim as x–> inf –> -inf

lim as x –> -inf –> -inf

Question 3

odd degree and positive leading coefficient

Answer 3

lim as x–> inf –> inf

lim as x–> -inf –> -inf

Question 4

odd degree and negative leading coefficient

Answer 4

lim as x –> inf –> -inf

lim as x –> -inf –> inf

Question 5

to find the limits at infinity of rational functions, we will divide every term in the function by the term in the denominator with the

Answer 5

highest power of X

Question 6

if one limit at infinity exists…

Answer 6

it equals the other limit

Question 7

Find the limit at infinity by dividing every term by the largest power in the denominator, and then find the limit of the numerator and then denominator. The limit of the numerator over the limit over the denominator equals the ________.

Answer 7

how to find the horizontal asymptote

Question 8

if x –> inf, we divide by the _____ ______ _____ of e^nx in the denominator

Answer 8

most positive power

Question 9

if x –> -inf, we divide by the ____ ______ ____ of e^nx in the denominator

Answer 9

most negative power

Question 10

if there is no “most positive” or “most negative” power in the denominator, we

Answer 10

do not divide, and go straight to observing the limit of the numerator and denominator

Question 11

to find holes, look for factors in the numerator and denominator that

Answer 11

divide completely out from the denominator

Question 12

to find vertical asymptotes, look for factors in the denominator that

Answer 12

remain after dividing common factors, and set equal to zero

Question 13

to find where on a graph it is discontinuous, find the

Answer 13

DOMAIN

Question 14

domain restrictions:

denominator must not equal

Answer 14

zero

Question 15

domain restrictions:

the argument of an even root must be

Answer 15

non negative, or greater than or equal to zero

Question 16

domain restrictions:

the argument of a log must be

Answer 16

positive, or greater than zero

Question 17

rules for continuity

Answer 17

cut off number =5

1) f(5) exists
2) lim as x–>5 exists
3) lim as x–> 5 equals f(5)

Question 18

slope of the secant line
difference quotient
average velocity

Answer 18

average rate of change also equals

Question 19

difference quotient

Answer 19

f(x+h)-f(x)/h

Question 20

instantaneous rate of change
limit of the slopes of secant lines
limit of the difference quotient

Answer 20

slope of the tangent line

Question 21

r(100)-r(75)/100-75

Answer 21

average rate of change

Question 22

slope of the tangent line
instantaneous rate of change
instantaneous velocity
limit of the difference quotient
limit of the slopes of secant lines

Answer 22

derivative f’

Question 23

three ways to say f is non-differentiable at x=a?

Answer 23

corner or cusp, discontinuity, vertical tangent line