Integrals
Derivatives
Defs & Theorems
Limits
Extrema and POIs
100
Solve the indefinite integral ∫ x^2dx
x^3/3 + C
100
f(x) = 2x^3
6x^2
100

What is average rate of change of f(x)?

(f(b) – f(a))/(b-a)


100
What is the limit as x approaches 3 of (5x^2-8x-13)/(x^2-5)?
What is 2
100

Find the critical point of the function f(x)=8x^3+81x^2-42x-8

x=-7,1/4

200
Solve the definite integral ∫ (3x+4)dx on the interval (0,6)
14
200
f(x) = xsinx
xcosx + sinx
200

What is instantaneous rate of change at f(x) or the slope of a tangent line to f(x) ?

definition of a derivative

200
What is the limit as x approaches 2 of (3x^2-x-10)/(x^2-4)?
What is 11/4 or 2.75
200

Find the maximum points of the function f(x)=(x^4)/3-6x^2+2

What is (0,2)

300
Integrate: ∫(3-x)^10dx
-(3-x)^11 /11 + C
300
f(x) = (x+7)/((x-6)(x+2))
-(x^2+14x-16)/((x-6)^2(x+2)^2)
300

1. f(a) exists

2. lim as x approaches a exists

3. f(a) = lim as x approaches a of f(x)

What makes a function continuous at x=a?

300
What is the limit as x approaches 0 of sin(5x)/3x
What is 5/3 or 1.67
300

Find the minimum point(s) of f(x)=(x^4)/3-6x^2+2

What is ( 3, -25) and ( -3 , -25)

400
Integrate: ∫(sinx + cosx)^2dx
x + sin^2x + C
400
f(x) = ln(7x^(2)e^(x)sinx)
(2/x) + 1 + cotx
400

Name the theorem:

If f is continuous on the interval (a,b) and differential on (a,b) such that f(a) = f(b), then there is at least one number c in the open interval (a,b) such that

f '(c) = 0


What is Rolle's Theorem?

400
What is the limit as x approaches 0 of (cos(2x)-1)/(cosx-1)?
What is 4
400

Find the point(s) of inflection of the function f(x)=x^3-3x^2-9x+7

What is (1,-4)

500
Integrate: ∫ x√(1+x^2)dx given x = tanθ
(1/3)(1+x2)^(3/2) + C
500
f(x) = (cosx)/(1+sinx)
-1/(1+sinx)
500

Name a theorem:

If f is continuous on a closed interval [a,b] and differentiable on (a,b), then there is a point c on (a,b) , such that 

f'(c)=(f(b)-f(a))/(b-a)

What is the Mean Value Theorem?

500
What is the limit as x approaches π/2 of (tan(2x))/(x-π/2)
What is 2
500

Find the point(s) of inflection of the function f(x)=2/(x^2)+1/x

What is (-6, -1/9)

M
e
n
u