final

Question 1

∫a^x dx

Answer 1

((a^x)/ln(a)) + c

Question 2

∫e^ax dx

Answer 2

((e^ax)/a) + c

Question 3

∫sec(x)tan(x) dx

Answer 3

sec(x) + c

Question 4

∫csc(x)cot(x) dx

Answer 4

-csc(x) + c

Question 5

∫sec^2 (x) dx

Answer 5

tan(x) + c

Question 6

∫csc^2(x) dx

Answer 6

-cot(x) + c

Question 7

∫(1/(1+x^2)) dx

Answer 7

arctan(x) + c

Question 8

∫(1/(√1-x^2)) dx

Answer 8

arcsin (x) + c

Question 9

∫tan(x) dx

Answer 9

-ln|cos(x)| + c

Question 10

F(x) + C

Answer 10

= ∫f(x) dx

Question 11

d/dx (position)

Answer 11

= velocity (v(t))

Question 12

d/dx (velocity)

Answer 12

= acceleration (a(t))

Question 13

Riemann summation right

Answer 13

i=1, n

Question 14

Riemann summation left

Answer 14

i=0, n-1

Question 15

ix

Answer 15

a+ delta(x)i

Question 16

FTC P1

Answer 16

F’(x) = f(x)

Question 17

FTC P2: area under curve from a to b

Answer 17

∫ f(x)dx = F(b) - F(a)

Question 18

indefinite integral

Answer 18

no given interval, will have function as answer (x’s in answer)

Question 19

definite integral

Answer 19

given interval, [a,b], and number as answer (no x’s)

Question 20

0/0 or ∞/∞

Answer 20

L’hopital rule

Question 21

definition of derivative, lim to 0

Answer 21

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

Question 22

definition of derivative, lim to a

Answer 22

(f(x) - f(a))/(x-a)), a is derivative of f(x)

Question 23

linearization

Answer 23

L(x) = f(a) - f’(a)(x-a)

Question 24

mean value theorem

Answer 24

continuous in (a,b)
differentiable on [a,b]
there exists a c in (a,b) such that f’(c) = (f(b) - f(a)) / (b-a))

Question 25

squeeze theorem

Question 26

extreme value theorem

Question 27

intermediate value theorem

Question 28

rolle’s theorem

Answer 28

continuous on [a,b]
differentiable on (a,b)
f(a) = f(b)
then there exists a c in (a,b) such that f’(c) = 0