Review Quizzes

Question 1

d/dx n^{x}

Answer 1

n^{x} ln(a)

Question 2

Integral n^{x} dx

Answer 2

n^{x} / ln(n) + C

Question 3

lim x->-∞ (4+3^{x})/1-5^{x})

Answer 3

4

Question 4

lim x->∞ [(2x+7)(x-3)]/(x^{2}-9)

Answer 4

2

Question 5

lim x->∞ (4+3^{x})/1-5^{x})

Answer 5

0 (BOBO)

Question 6

IVT conditions

Answer 6

1. The function is continuous on [a,b]
2. F(c) is between f(a) and f(b)

Question 7

IVT conclusion

Answer 7

There exists a value c in [a,b] such that f(c) is between f(a) and f(b)

Question 8

f’(a) as a limit of a difference quotient

Answer 8

lim x->a f(x)-f(a) / x-a

       OR

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

Question 9

d/dx sqrt(cosx)

Answer 9

-sinx / 2 * sqrt(cosx)

Question 11

d/dx tan^(3) x

Answer 11

3(tanx)^(2) (sec^(2) x

Question 12

Given V=1/3(pi * r^(2) * h) Find dV/dt in terms of r and dr/dt if r/h = 1/2

Answer 12

dV/dt = 2 * pi * r^(2) * dr/dt

Question 13

MVT conditions

Answer 13

1. Function is differentiable on (a,b)
2. Function is continuous on [a,b]

Question 14

MVT conclusion

Answer 14

There must exist at least one value c in (a,b) such that f’(c) = f(b)-f(a) / (b-a)

Question 15

EVT condition(s)

Answer 15

Function is continuous on [a,b]

Question 16

EVT conclusion

Answer 16

There must be an absolute maximum and minimum on [a,b]

Question 17

First derivative test for local max

Answer 17

f’(c) = 0 or undefined and f’(c) switches from + -> - @ c, f(c) is a local max

Question 18

Second derivative test for local max

Answer 18

If f’(c) = 0 and f’‘(c) < 0, then f(0) is a local max.

Question 19

A graph is concave up on an open interval if…

Answer 19

f’‘(x) > 0 OR f’(x) is increasing on the interval

Question 20

Critical value

Answer 20

f’(c) = 0 or f’(c) is undefined

Question 21

A function f, has an inflection point at x=c if…

Answer 21

f’(c) changes from increasing to decreasing or decreasing to increasing at x=c

Question 22

A function f, has an inflection point at x=c if…

Answer 22

f’‘(c) changes from positive to negative or negative to positive at x=c