calc exam 2

Question 1

d/dx arcsinx

Answer 1

1/ sqrt(1-x^2)

Question 2

d/dx arctan

Answer 2

1/(1+x^2)

Question 3

d/dx arcsec

Answer 3

1 / |x|*sqrt(x^2 - 1)

Question 4

d/dx arccos

Answer 4

-1 / (1-x^2)

Question 5

d/dx arccotx

Answer 5

-1 / (1+x^2)

Question 6

d/dxarccscx

Answer 6

-1 / |x| sqrt(x^2-1)

Question 7

Rolles theorem

Answer 7

if:
1. fcn is diff’ble on (a,b)
2. fcn is continuous on (a,b)
3. f(a) = f(b)
then exists some c where f’(c) = 0

Question 8

mean value theorem

Answer 8

if
1. fcn diff’ble on (a,b)
2. fcn continuous on (a’b)
then exists some c where
f’(c) = (f(b) - f(a)) / ( b - a)
or
f’(c)(b-a) = f(b) - f(a)

Question 9

compound interest formula

Answer 9

A(sub 0) * (1 + r/n)^(nt)

Question 10

ln(f(x))

Answer 10

f’(x) / f(x)

Question 11

linearization formula

Answer 11

L(x) = f(a) + f’(a)(x-a)

Question 12

ln(1)

Answer 12

0

Question 13

e^0

Answer 13

1

Question 14

lnx graph

Answer 14

y = 0 vertical asymptote
kind of u-shaped concave down

Question 15

e^x graph

Answer 15

y = 0 horizontal asymptote
kinda right angle u shaped

Question 16

list of indeterminate forms

Answer 16

0/0
infinity/infinity
0^(0)
0*infinity
1^(infinity)
infinity^(0)
infinity - infinity