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
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
If f is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum of [a,b].
What is the extreme 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