Differentiation and integration
Formulas
Parametric
Polar
Series and Sequences
100
The maximum value of sin (x) from 0<x<Π
What is Π/2
100
The formula for a geometric series
What is a(sub)1 /1-r
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
Macleran series for e^ around x=0 the first three non-zero terms
What is 1+x+x^2 /2
200
Y=sin(3x), dy/dx =
What is -3cos(3x)
200
Length of the curve
What is integral from a to b of √(1+dy(/dx)^2)
200
Length of a vector
What is √(a^2 + b^2 )
200
Area of polar curve
What is integral from a to b of 1/2(f(θ))^2 d θ
200
Value of the summation from n=1 to infinity of 2^(n+1) / 3^n
What is 4
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
Length of a vector
What is √(a^2 + b^2 )
300
Length of of a parametric
What is integral from a to b of √(f'(t)^2 + g'(t)^2 dt
300
The slope of the line tangent to r=2 θ at the point θ=Π/2
What is -2/Π
300
The value of the summation from 0 to infinity of (-2/3)^n
What is 3/5
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 maclaurin series for fn (0)=(-1)^n (n+1)/(n+2)2^n
What is (1/2) - (1/3) x + (3/16) x^2 - (1/10) x^3
500
The value of f'(x) if f(x)=arccos(x^2)
What is -2x/(√(1-x^4))
500
Logistic differential equation
y=L/1+Ae^(-kt)
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
The interval of convergence for the summation from n=1 to infinity of (x+3)^2n / n
What is 2<x<4
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