chapter 2 (limits)

Question 1

v average

Answer 1

x2-x1/y2-y1

Question 2

right sided limits

Answer 2

what x approaches as it approaches from the right

Question 3

left sided limits

Answer 3

what x approaches fro teh left

Question 4

first way to attempt to take a limit

Answer 4

plug it in

Question 5

lim (a+b)

Answer 5

lim a +lim b

Question 6

lim a-b

Answer 6

lim a - lim b

Question 7

lim ca

Answer 7

a lim c

Question 8

lim (ab)

Answer 8

(lim a)(lim b)

Question 9

lim (a/b)

Answer 9

lim a/lim b

Question 10

lim a^n

Answer 10

(lim a)^n

Question 11

lim a^(a/b)

Answer 11

(lim a)^a/b

Question 12

squeeze theorem

Answer 12

f

Question 13

vertical asymptotes

Answer 13

when the denominator +0

Question 14

hole

Answer 14

when the numerator and denominator cancel out

Question 15

horizontal asymptotes

Answer 15

if denominator degree is larger than numerator then asymptote is 0

if they equal it is the fraction of there coefficients

if degree of numerator is larger then no HA

Question 16

slant asymptotes

Answer 16

occur when the degree of the numerator is larger than the denominator

Question 17

polynomial long devision

Answer 17

1. write the denominator outside the division symbol and the numerator in it
2. ask what multiplies by the first value in the denom to get the first value of the numerator
3. subtract after this
4. with the new line ask the same thing again
5. cancel until you get the remainder. you dont need it for slant asymptotes.

Question 18

lim (x to inf) e^x

Answer 18

inf

Question 19

lim (x to -inf) e^x

Answer 19

0

Question 20

lim (x to inf) e^-x

Answer 20

0

Question 21

lim (x to -inf) e^-x

Answer 21

inf

Question 22

lim (x to inf) ln x

Answer 22

inf

Question 23

lim (x to 0+)

Answer 23

-inf

Question 24

for a point to be continuous what must be true

Answer 24

it must be defined
limit must exist
value of f(a) = limit at that point

Question 25

a rational function is continuous for all values P/q wehn

Answer 25

q does not equal 0

Question 26

if f is cont and g is cont then F(g(x))

Answer 26

is cont

Question 27

if g is cont at a and f is cont at g(a)

Answer 27

then the limit is lim(x to a) is f(lim g(a))

Question 28

if a function is continuous on and interval then the inverse is

Answer 28

also continuius

Question 29

intermediate value theorem

Answer 29

f is continuous from a to b and L is a number in between f(a) and f(b) then there exists one number c (between a and c) in that f(c) is L

Question 30

how to find epsilon given delta is [x-a]<1

and {fx-L]

Answer 30

look at graph. find the values vertically form a+1 and a-1
then find the horizontal equivalent

the difference from the horizontal number at L

Question 31

how to find delta given epsilon is {fx-L]<1

and [x-a]

Answer 31

look at graph. find the values horizontalv form L+1 and L-1
then find the vertically equivalent

the difference from a to its extremeties is delta

Question 32

how to do a limit with the formal definition

ex prove that lim (4x-15) =1

Answer 32

1. set as [f(x)-L]