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Differentiation and integration
Formulas
Parametric
Polar
Random
100
The maximum value of sin (x) from 0<x<Π
What is Π/2
100
The formal definition of a derivative
What is lim h-> 0 f(x+h)- f(x)/h
100
2nd derivative of a parametric
What is (d(dy/dx)/dt)/(dx/dt)
100
In polar x= and y=
What is rcos θ and rsin θ
100
The differentiation by parts formulas
What is integral(udv) = uv - integral(vdu)
200
Y=sin(3x), dy/dx =
What is -3cos(3x)
200
Length of the curve (not parametrics)
What is integral from a to b of √(1+dy(/dx)^2)
200
The tangent line(s) of x=t^5 - 4t^3 and y=t^2 at (0,4) are...
y=4 +/- 1/8x
200
Area of polar curve
What is integral from a to b of 1/2(f(θ))^2 d θ
200
The saying to remember the quotient rule
What is lodhi - hidlo all over lolo
300
The length of the curve y=x^4 from x=1 to x=5
What is the integral from 1 to 5 of √(1+16x^6) dx
300
Arc Length for parametrics
What is √((dy/dt)^2 + (dx/dt)^2 )
300
The arc length of x=3sin(3t) and y=3cos(3t) from 0<=t<=2pi
What is 18pi
300
The slope of the line tangent to r=2 θ at the point θ=Π/2
What is -2/Π
300
Find the area inside the curve r=3cos(theta) and outside r=1+cos(theta)
What is pi
400
Dy/dx of x^2/x^3
What is 1/x^2
400
Average value of a function
What is 1/(a+b) • the integral from a to b of f(x) dx
400
Values t is at rest if x=t^3 -3t^2 and y= 2t^3 -3t^2 -12t
What is -1,0,and,2
400
The total area enclosed by r=sin^2 (θ) Set up but do not evaluate
What is the integral from 0 to Π of sin^4 θ d θ
400
The set up for the integral for the volume of the solid obtained by rotating the region bounded by y = cuberoot(x), x=8, and the x-axis about the x-axis
What is pi*integral(cuberoot(x)^2)dx from 0 to 8 OR 2pi*integral(y*y^3)dy from 0 to 2
500
The value of f'(x) if f(x)=arccos(x^2)
What is -2x/(√(1-x^4))
500
Identity for cos(A+B)
cos(A)sin(B) + cos(B)sin(A)
500
D^2 y/dx^2 of x=4-2t y= ln4t
What is 1/4t^2
500
The length of the polar curve r= e^ θ
What is √(2)•(e^(2Π) -1)
500
Prove that (cf(x))' = c(f'(x))
Using formal definition of a derivative