Limits
lim x->2 (x^2 +2x -8)
What is 0?
d/dx 4x^2 +9x-3
int sin^2 dx
1/2 (x- 1/2 sin(2x))+c
What is the area between the function f(x) = 4x and the x-axis on the interval [0,5]
What is 50?
What are the critical points of f(x)= 5x^4 - 20x^3 + 4
What is x=0, x=3 ?
What is -1?
d/dx lnx
1/x
int_0^pi secx*tanx - cotx dx
Find the area enclosed by the curves f(x)=x-6 and g(x)=x^2 -12 on the interval [-2,3].
What is 125/6 ?
What is the concavity of f(x)=(x/3)^3 + x when x<0
What is concave down?
lim x->pi ((sin^2 x - cosx)/(x^2))
d/dx (sin^2 x)/(cosx +2x^2)
(sin2x * (cosx+2x^2) -(-sinx + 4x)sin^2 (x))/(cosx +2x^2)^2
int 2x^2 cosx dx
2(x^2 sinx - 2(-xcosx +sinx)) +c
Annual sales (in millions) of a phone company are modeled by the function f(t) = 0.2t^2 + .15t + 2.9 per year, where t is the number of years. How many phones are sold after 7 years?
What is 46.84166 million phones?
A rectangular field must be enclosed with 500 feet of fencing, one side of the fence is against a house so it doesn't require any fencing. What fence dimensions will maximize the area enclosed by the fence?
What is 125 ft x 250 ft?
lim x->0 ((x)/(2-sqrt(x+6)))
What is 0?
The implicit derivative of 6xy^2 = x-2y
What is y=(1-6y^2)/(2(1+6xy)
int_-2^0 x sqrt(3+x^2) + 3/(6x-1)^2 dx
1/3 (3^3/2 - 7^3/2) + 6/13
rotate the region between 0 and sin x with 0<x<pi around the x-axis
What is pi^2 /2 ?
Use the linear approximation of f(x)=3x^4 +12x^3 +2x at x=1 to find the value of f(x) at the value x=2.
lim x->0 ((cos(pi cos^2 (x))/(x^2))
What is negative infinity?
The second derivative of 4xy^2 -x^2 = 2xy +y
What is (-24y^2 +32y^3 + 4y-2)/(20x^2 + 8x + 64x^2 y^2 + 32xy^2 - 32x^2 y - 8y+3) ?
int t^7 (8+ 3t^4)^8 dt
1/36 (1/10 (8+3t^4)^10 - 8/9 (8+3t^4)^9)+c
Find the volume of the solid whose base is the region bounded by the lines y = -x^2, x = 0, and y = 0, if the cross sections taken perpendicular to the x‐axis are semicircles.
What is 128pi/15 ?
Determine all the number(s) c which satisfy the conclusion of Mean Value Theorem for f(x)=3x^(3)-12x^(2)+2x on [1,4]
What is (4+sqrt(19)/3