Chapter 1

Question 1

F(x) increases or decreases without bound as x approaches c

Answer 1

DNE

Question 2

F(x) oscillates between two fixed values as x approaches c

Answer 2

DNE

Question 3

F(c) does not equal the limit at f(c)

Answer 3

The limit does exist

Question 4

Constant functions

Answer 4

Continuous over domain

Question 5

Polynomial function

Answer 5

Continuous over domain

Question 6

Rational Function

Answer 6

Continuous over domain

Question 7

Radical Functions

Answer 7

Continuous over domain

Question 8

Trig Functions

Answer 8

Continuous over domain

Question 9

Let c be a real number and f(x)=g(x) for all x ≠ c in an open interval containing c. If lim as x approaches c g(x) exists, then…

Answer 9

then lim of f(x) as x approaches c has that same value.

Question 10

Lim as x approaches 0 sin x/x=

Answer 10

=1

Question 11

Lim as x approaches 0 1-cos x/x=

Answer 11

=0

Question 12

Removable discontinuity

Answer 12

Holes

Question 13

Nonremovable discontinuity

Answer 13

Asymptotes

Piecewise

Question 14

A function is continuous on x=c on the closed interval [a,b] if

Answer 14

If it is continuous on the open interval (a,b) and lim as x approaches c from the left and right is equal with f(c)

Question 15

If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then

Answer 15

Then there is at least one number c in [a,b] such that f(c)=k

Question 16

Vertical Asymptotes

Answer 16

Factors on the denominators that are not repeated on the numerator

Question 17

Given that lim as x approaches c f(x)=∞ and lim as x approaches c g(x)=L

Lim as x approaches c f(x) + g(x)=

Answer 17

∞ (DNE)

Question 18

F(x) approached a different value from the left and right side of c

Answer 18

DNE

Question 19

Given that lim as x approaches c f(x)=∞ and lim as x approaches c g(x)=L

Lim as x approaches c f(x) · g(x)=

Answer 19

∞, L > 0 (DNE)

Question 20

Given that lim as x approaches c f(x)=∞ and lim as x approaches c g(x)=L

Lim as x approaches c f(x) · g(x) =

Answer 20

-∞, L

Question 21

Given that lim as x approaches c f(x)=∞ and lim as x approaches c g(x)=L

Lim as x approaches c g(x)/f(x)=

Answer 21

0

Question 22

∞/∞

Answer 22

Indeterminate form

Question 23

0/0

Answer 23

Indeterminate form

Question 24

Degree of numerator and denominator is the same

Answer 24

HA at y= (ratio of leading coefficients)

Question 25

Degree of denominator is larger

Answer 25

HA at y=0

Question 26

Degree of numerator is larger

Answer 26

No HA

Question 27

If r is a positive rational number and c is any real number then,

Lim as x approaches ∞ c/x^r=

Answer 27

0

Question 28

If r is a positive rational number and c is any real number then,

Lim as x approaches -∞ c/x^r=

Answer 28

0