Whole Year

Question 1

What is the limit definition of an integral?

Answer 1

Question 2

What is the limit defintion of a derivative?

Answer 2

Question 3

What is the derivative of an inverse function with a variable of y?

Answer 3

Question 4

What is the limit as x approaches zero of (sin(x))/x ?

Answer 4

Question 5

What does intermediate value theorem state about continuous functions?

Answer 5

If f is continuous on an interval [a,b], and a number k is between f(a) and f(b), there will be at least one number c such that f(c)=k.

For example, any continuous function over [a,b] for which f(a) is negative and f(b) is positive, there must be at least one x intercept on the interval [a,b].

Question 6

What are the derivatives of:

sin(x)

cos(x)

tan(x)

Answer 6

cos(x)

-sin(x)

sec²(x)

Question 7

True or false?

Answer 7

False! Never forget the dx on an integral!

Question 8

“a” is a function representing the acceleration of a particle with linear motion. If the particle’s position at t=0 is +24 units from the origin, write a function for the particle’s position at any time “t”.

a(t)=-cos(t)+6

Answer 8

s(t)=cos(t)+3t²+23

Question 9

What is the derivative of e^x?

Answer 9

e^x

Question 10

According to the fundamental theorem of calculus, what is this equation equal to?

Answer 10

F(b)-F(a), F being the antiderivatve of f.

Question 11

According to the Fundamental Theorem of Calculus, what does this equation equal?

Answer 11

f(x)

Question 12

Find the limit as x approaches zero.

Answer 12

2

Question 13

Find the limit as x approaches infinity.

Answer 13

Infinity.

Question 14

For what value of x does the function f(x)=2x³-3x²-12x have a relative minimum?

Answer 14

2

Question 15

R is a differentiable function in terms of t, that gives how much rain has fallen over the course of a 3 day period. t is in hours. What is represented by R’(36)?

Answer 15

The rate at which the amount of rain fallen is changing at the end of the 36th hour (instantaneously).

Question 16

Find the area between f(x)=2x-x² and g(x)=x²

Answer 16

1/3

Question 17

Use summation notation to write the right Riemann sum for n, for the integral from 0 to 3 of (2x-5) dx.

Answer 17

Question 18

Find the second derivative of f(x)=x⁴-2x³+cos(-2x)

Answer 18

f’‘(x)=12x²-12x+4cos(-2x)

Question 19

Find the first derivative of f(x)=log₃(x²)

Answer 19

Question 20

Find the derivative of f(x)=cos(x)sin(x)

Answer 20

-sin²x+cos²x

Question 21

What is the derivative of f(x)=xⁿ?

Answer 21

f’(x)=nx^n-1

Question 22

What is the definition of an even function?

Answer 22

f(-x)=f(x)

Question 23

What is the definition of an odd function?

Answer 23

f(-x) = -f(x)

Question 24

Use the formula for the volume of a sphere to find the formula for the surface area. (Hint: V’=Area)

V=(4/3)πr³

Answer 24

A=4πr²

Question 25

Find the derivative of (x²-2)/(x³)

Answer 25