final exam

Question 1

what rule do we use when we try to evaluate and it gives 0/0 or inf/inf

Answer 1

L’hopital rule

Question 2

what happens when denominator is bigger than numerator

Answer 2

it will be 0

Question 3

ln(x)

Answer 3

1/x

Question 4

cos(0)

Answer 4

1

Question 4

d/dx of cosx

Answer 4

-sinx

Question 4

sin(0)

Answer 4

0

Question 4

d/dx of sinx

Answer 4

cosx

Question 5

in limits, sinx/x

Answer 5

its 1

Question 5

what to do with LH

Answer 5

keep find doing derivative until it does not give 0/0 or inf/inf

Question 6

a^3 - b^3

Answer 6

(a-b)(a^2+ab+b^2)

Question 7

in limits, tanx

Answer 7

its sinx/cosx

Question 8

in limits, if polynomials

Answer 8

ignores insignificant terms

Question 9

in limits, if we look for HA

Answer 9

we use limit x->inf

Question 10

in limits, if we look for VA

Answer 10

we use limit x->0

Question 11

any power of 0

Answer 11

= 1

Question 12

loga (b) = c

Answer 12

= a^c b

Question 13

ln(1)

Answer 13

0

Question 14

squeeze theorem

Answer 14

h(x) <_ f(x) <_ g(x)

Question 15

d/dx of x

Answer 15

= 1

Question 16

d/dx of e

Answer 16

= 0

Question 17

d/dx of ln(u)

Answer 17

= u’/u

Question 18

log,diff and inv trig: d/dx of a^u

Answer 18

= a^u . u’ . ln (a)

Question 19

d/dx of e^u

Answer 19

= e^u . u’

Question 20

in piecewise functions, if there’s a letter except x and y

Answer 20

have to make it the same and that letter = ?

Question 21

3 steps continuity test

Answer 21

1. f(a) is defined
2. lim x->a f(x) exist
3. lim x->a f(x) = f(a)

Question 22

if step 2 fails in “3 steps continuity test”

Answer 22

it will be a jump discontinuity

Question 23

if step 3 fails in “3 steps continuity test”

Answer 23

it will be a hole discontinuity

Question 24

definition of derivatives

Answer 24

lim h->0 f(x+h) - f(x) / h

Question 25

d/dx of tanx

Answer 25

sec^2x

Question 26

d/dx of cotx

Answer 26

-csc^2x

Question 27

d/dx of secx

Answer 27

secxtanx

Question 28

d/dx of cscx

Answer 28

-cscxcotx

Question 29

eqn of tangent line

Answer 29

y-y1 = m (x-x1)

Question 30

when look for eqn of tangent line, how to find y

Answer 30

f(x) will be y and plug x in the f(x) function.

Question 31

when look for eqn of tangent line, how to find m

Answer 31

m is f’(x) of f(x)

Question 32

quotient rule

Answer 32

(hi)(d’lo) - (lo)(d’hi) / lo^2

Question 33

product rule

Answer 33

uv’ +vu’

Question 34

chain rule

Answer 34

f(g(x)) = f’(g(x)) . x’

Question 35

d/dx of cot(g(x))

Answer 35

-csc^2(g(x)) . (g’(x))

Question 36

d/dx of arctan g(x)

Answer 36

(1/ 1 + g(x)^2) . g’(x)

Question 37

d/dx of arcsin g(x)

Answer 37

(1/ sqrt( 1- g(x)^2) . g’(x)

Question 38

d/dx of arccos g(x)

Answer 38

(-1/ sqrt( 1- g(x)^2) . g’(x)

Question 39

steps in Logarithmic Differentiation

Answer 39

1. put ln both sides
2. ln multiply with the eqn
3. put d/dx
4. solve

Question 40

steps of implicit difference

Answer 40

1. deriv both sides
2. rearrange and factor

if looking for slope of an eqn: plug numbers in

(whenever y is affected, there will d/dx next to it)

Question 41

inverses functions

Answer 41

exchange with y and x