States that if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain its maximum and minimum value, each at least once.
What is Extreme Value Theorem?
100
(x^2 -81) equals this option:
A. (x+18)(x-18)
B. (x+9)(x+9)
C. (x-9)(x-9)
D. (x+9)(x-9)
What is D. (x+9)(x-9)?
200
The limit as x approaches 7 of (x^2 +11)/(x-2)
What is 12?
200
∫ from 0 to 2 of 4xdx
What is 8?
200
(2x)(x+4)^2
What is 4x(x+4)+2(x+4)^2?
200
States that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero.
What is Rolle's Theorem?
200
(x+5)(3x+7) equals this option:
A. (3x^2 +35)
B. (3x^2 +22x+ 35)
C. (3x^2 +8x+ 35)
D. (3x^3 +22x^2+ 35)
What is B. (3x^2 +22x+ 35)?
300
The limit as x approaches infinity of (3x^4 +9)/(2x^4 -x)
What is 3/2?
300
The u of ∫ 9x^2 (3x^3)dx
What is 3x^3
300
The acceleration when x=2 and the car's velocity can be measured by 3x+4x^3
What is 51?
300
Shows that an indefinite integration can be reversed by a differentiation.
i.e. The derivative of the integral of f(x) is equal to f(x)
What is The First Fundamental Theorem of Calculus?
300
(2x)/(x^.5) equals this option:
A. 2x(x^.5)
B. 2x^(-2)
C. 2x(x^.5)^-1
D. (-x)/(2x^2)
What is C. 2x(x^.5)^-1?
400
The limit as x approaches infinity of (6x)/(5x+7)
What is 6/5?
400
The limits in term of u of ∫ from 3 to 5 of 4x(2x^2)dx
What is (18,50)?
400
The tangent line of f(x)=3x^4 +4x at x=2
What is y-56=100(x-2)?
400
Allows one to find the definite integral of a function by using any one of its infinitely many antiderivatives.
i.e. the integral from a to b of f(x) equals g(b)-g(a), such that f(x)=g'(x)
What is Second Fundamental Theorem of Calculus?
400
(27x^7)^1/3 equals this option:
A. (27x)^7/3
B. (9x)^7
C. (9x)^7/3
D. (27x)^3/7
What is A. (27x)^7/3 ?
500
The limit as x approaches 0 of (3x^2)/(4x^2)
What is 6/8 or 3/4?
500
∫ from 1 to 2 of 8x(4x^2)dx
What is 8?
500
The dy/dx of 36x^3 -21y^2=45
What is (108x^2)/(42y) or (54x^2)/(21y)?
500
States that given a curve between two endpoints, there is at least one point at which the tangent to the curve is parallel to the line through its endpoints.
What is Mean Value Theorem?
500
e^(52x+yc) equals this option:
A. 52x^e +yc^e
B. e^(52x) +yc
C. e^(52x) e^(yc)
D. ln 52x+yc