Unit 1: Limits, Continuity, Derivatives Unit 2: Integrals Unit 3: Differential Equations Unit 4 & 5: Sequences & Series Unit 6: Parametric & Polar Equations
What is the limit definition of a derivative?
lim f(x+h)-f(x)
h->0 -----------
h
What is u-substitution?
The reverse chain rule for integration.
What is a differential equation?
An equation that involves the derivative of a function, as well as the function itself.
What is the radius of convergence?
The ratio test is commonly used to determine this property of a power series.
What is a circle?
The shape formed by the polar equation r=2cos(theta)
What is the chain rule?
d
-- f(g(x)) = f'(g(x))*g'(x)
dx
What is integration by parts?
int(u)dv = uv - int(v)du
What is separation of variables?
A method used to solve a differential equation by integrating both sides after separating variables.
r
This formula gives the sum of an infinite geometric series with the first term a and the common ratio r where
What is y = 2sqrt(x)+1?
The cartesian equation, given the parametric equations x = t^2 and y = 2t + 1
What is f"(x)?
Shows the concavity of function f(x). It's zeroes represent its inflection points.
What is the order to choose of the u value in integration by parts?
Logs
Inverse
Algebraic
Trig
Exponential
What is y = x^3+C?
In the terms of a differential equation it is the general term of dy/dx = 3x^2
What is 2?
This is the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + ...
What is x^2+(y-1)^2=1?
The rectangular form of r=2sin(theta).
When is a function continuous, but not differentiable?
When the function experiences a cusp, or a corner.
What is the disk method?
V = pi * int (R(x)^2)dx
a->b
What is y = Ce^sin(x)?
This is the solution to the separable differential equation dy/dx = y * cos(x)
What is 1?
This is the radius of convergence for the power series
oo
__
> x^n/n
---
n=1
What is an ellipse with equation x^2/9 + y^2/16 = 1?
Given the parametric equations x = 3cos(t) and y = 4 sin(t), the equation in cartesian coordinates, and its shape.
What is f'(x)=x^x(ln(x)+1)?
The derivative of f(x)=x^x
What is the derivative of f(x) = 3sin^2(x)+c?
f'(x) = 6sin(x)cos(x)
What are P=0 and P=100?
These are equilibrium solutions for the population model dP/dt = 0.5P(1-P/100)
What is
oo
____
> x^n/n!
-----
n=0
This is the Taylor series expansion of e^x centered at x=0
What is 2pi/3?
The area enclosed by one loop of the polar curve r = 2sin(theta)

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