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Limits
Rates of Change
Derivatives
Trig Functions
Higher Order
100
lim(x→2) (x^2+2x+1)
What is 9?
100
Given the function f(x)=x^2+3x+4, find the average rate of change from x=2 to x=4.
What is 9?
100
g(x)= x^3+4x^2+3x+2
What is 3x^2+8x+3
100
Find the derivative of the function g(x)=3sinx+4x
What is 3cosx+4?
100
If f(x)=x^4+2x^3-3x+1, find f'''(x).
What is 24x+12?
200
lim(x→0) (sin2x)/x
What is 2?
200
Let f(x)= 3x^3+4x+1. Find the instantaneous rate of change when x=2.
What is 40?
200
h(x)= 4/(x^2)+sqrt(x)
What is -8x^-3+1/2x^(-1/2)?
200
Find f'(x), if f(x)=(x^2)cosx
What is -(x^2)sinx+2xcosx?
200
If f'(x)=sqrt(x), find f'''(x).
What is (-1/4)x^(-3/2)?
300
lim(x→3) (x^2-5x+6)/(x^2-9)
What is 1/6?
300
Find the equation of the tangent line to the curve y=2/(x^2), when x=3.
What is y-2/9 = -4/27(x-3)
300
f(x)=(x^2-x)(4sqrt(x)+2)
What is (x^2-x)(2x^(-1/2))+(4sqrt(x)+2)(2x-1)
300
Find the equation of the tangent line to the curve g(x)=2cosx+3x at the point where x=π.
What is y-(-2+3π)=3(x-π)?
300
Find g''(x) if g(x)=cscx.
What is (cscx)^3-(cotx)^2(cscx)?
400
lim(x→0) (tanx)/(xcosx)
What is 1?
400
Find the instantaneous rate of change of the function g(x)=x^2sinx, when x=π.
What is -π^2?
400
f(x)= (x^3+4x)/(sqrt(x)+1)
What is ((sqrt(x)+1)(3x^2+4)-(x^3+4x)(1/2x^(-1/2)))/((sqrt(x)+1)^2)?
400
Find h'(x) if h(x)= (sqrt(x)+x^2)/(tanx+1).
What is ((tanx+1)(1/2x^(-1/2)+2x)-(sqrt(x)+x^2)(sec^2(x))/((tanx+1)^2)?
400
If h(x)=1/(x^3)-2sqrt(x)+3x^3, find h'''(x).
What is -60(x^-6)-(3/8)x^(-5/2)+18?
500
lim(x→0) (sqrt(x+9)-3)/x
What is -1/9?
500
What is the slope of the tangent line of the curve y=x/cosx at the point where x=0.
What is 1?
500
h(x)=(1+2/x^3)(4/(3x^3)+3x^2)
What is (1+2/x^3)(-4x^-4+6x)+(4/(3x^3)+3x^2)(-6x^-4)?
500
Find the derivative of (x+1)/((x^2)sinx).
What is ((x^2)sinx-(x+1)((x^2)cosx+2xsinx))/((x^2)sinx)^2?
500
Find f''(x), if f(x)=secx+cscx
What is (secx)^3+(tanx)^2(secx)+(cscx)^3-(cotx)^2cscx?