What is the limit as x approaches 5 of
f(x) = 12x - 20?
40
100
∫25x^4 – 4x dx
5x^5 - 2x^2 + c
100
Find the area of the region between the graphs of f(x) = 3x^3 - x^2 - 10x and g(x) = -x^2 +2x
24
100
The general solution to the differential equation y=2sinx is...
y= 1/ (cos x +c)
200
Find the Derivative of f(x)= 4x^3 - x^(1/2)
f'(x) = 12x^2 -.5x^(-1/2)
200
What is the value of the limit as x approaches -1 of
(x^2-3x-4) / (x^2-1)?
5/2
200
∫9xe^(3x^2+1) dx
1.5e^(3x^2+1) + C
200
Let R be the region between the function
f(x) = x^3 +6x^2+10x+4, the x-axis, and the lines x=0 and x=4. Using the Trapezoidal Rule, compute the area when there are four equal intervals.
296
200
What value of c on the closed interval [1,3] satisfies the Mean Value Theorem for Integrals for f(x) = 2 ln x?
c = 1.912
300
Find the Derivative of √(4x-3)
2(4x-3)^(-1/2)
300
What is the limit as x approaches 8 + of 1/(x+8)?
1/16
300
∫cos(7t+3) dt
1/7 sin (7t+3) + c
300
A solid is generated by revolving the region bounded by the x-axis, the line x=5, and the function y=ln x around the x axis. The volume of the solid is...
15.259
300
If f(x) = 3x^3 + 5x and g(x) = f inverse of x, what is g'(8)?
1/14
400
Find the derivative of f(x) = (x-2) (3x^2-6x)
f'(x) = (x-2)(6x-6) + (3x^2-6x)
400
What is the one sided limit as x approaches 0 + of 2/(sin x)?
infinity
400
What is f(x) if f'(x) = 2x/ (x^2-1) dx and f(2)=0 ?
f(x) = ln I X^2-1 I - ln 3
400
If k>1, the area under the curve y=kx^2 from x=0 to x=k is...
1/3k^4
400
If tan y + x^3 = y^2 +1 and dx/dt = -2, what is the value of dy/dt at the point (1,0)?
6
500
If 2y^3 - 3xy + x^2 = 4, then dy/dx =
dy/dx = -2x / (6y^2 -3)
500
What is the limit as x approaches 0 of (sin3x) / (sin5x)?
3/5
500
∫1/(16+x^2) dx
1/4tan^-1(x/4) + C
500
A solid has its base in the xy-plane, bounded by the x-axis, the y-axis, and the function y=3-x^5. If cross sections taken perpendicular to the x-axis are semicircles whose diameters are in the xy-plane, what is the volume of this solid?
3.335
500
If h"(x) = e^(x-1) (2x-1)^2 (x-3)^3 (4x+5), then h(x) has how many points of inflection?