Integrals
Derivatives
Misc Theorems
Limits
Misc Problems
100
Solve the indefinite integral ∫ x^2dx
x^3/3 + C
100
f(x) = 2x^3
6x^2
100
(f(b) – f(a))/(b-a)
What is the formula for the average rate of change of f(x)?
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
Instantaneous rate of change at f(x) or the slope of a tangent line perpendicular to f(x)
What is the 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
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

What is the largest island in the world?

Greenland

500

What animal is known to laugh and has been proven to have a sense of humor?

Rats

500

What year did Mrs. M graduate from collage?

2005

500

What is USA national flower?

Rose

500


The Coca-Cola brand offers over ....... different beverages

3,500

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