Find the derivative of the function
y=x^5-1/8 x^2+1/4 x
What is 5x^4-x/4+1/4?
100
Use the Chain Rule to solve y=(2x-3)^4 when x=1 and find the new equation
What is y-1=1/8(x-1)?
100
1. The radius of a circle is icreasing at a rate of 4cm^2/sec. Find the rate of the change of the area when the radius is 10cm.
What is 80π cm^3?
100
Use the Fundamental theorem to evaluate the integral.
From 1 to -1 (X^2+3)dx
What is 20/3?
100
∫ (2x-3)^7 dx
What is (2x-3)^8/16?
200
Find the derivative of the function
y=tanx/2x^3
What is (xsec^2x-3tanx)/2x^4?
200
x^3*y^3+y^3=9 at the point (2,1)
What is -12/19?
200
Describe a) the intervals where the function is increasing/decreasing b) the type of concavity c) and points of inflection for the equation: f(x)= 3x^3-5x^2-8
What is a) increasing (-∞,0)U(10/9,0)
b)concave up
c)x=0, 10/9?
200
Find the RRAM value for (x^3+2)
What is 108?
200
∫ cos(3x) dx
What is sin3x/ 3?
300
Find the derivative of the function
y=(x^-2)(cosx)-4x^-3
What is (12-2xcosx-x^2sinx)/x^4?
300
y=x^2csc(5x)
What is 2x(csc(5x))+x^2(-csc(5x)cot(5x))*5?
300
Find all points of inflection on the graph of
f(x)= 1/12x^4-2x^2+15
What is x=+-2?
300
Find the average value of f(x)=2x^2+3 on the interval [0,2]
What is 17/3?
300
∫ √6+2x dx
What is (2u^3/2)/3?
400
Find the coordinates of all points on the (a) tangent and (b) normal to the curve at the indicated point
y=8x^-2, x=2
What is (a) y-2=-2(x-2)
(b) y-2=(1/2)(x-2)?
400
y=ln(1+e^x)
What is (e^x/1+e^x)?
400
The volume of a cube is expanding at a rate of 60cm^3/sec. How fast are the edges changing when the edges are each 6cm?
What is ds= 5/9cm/sec?
400
∫(4 to 0) x^2*√ 2
What is 256/7?
400
π/2
∫ (sinΘ dΘ)
π/6
What is Θ=(√ 3)/2?
500
Find an equation for the (a) tangent and (b) normal to the curve at the indicated point
y=4+cotx-2cscx, x=π (pi)
What is (a) y=-x+(π/2)+2
(b) y=x-(π/2)+2?
500
y=tan(2x) at x=π/3 (pi)
What is y+√3=8(x-π/3)?
500
Find the critical point for the function f(x)=-4x^4+3x^3