Derivatives
The derivative of ex
What is ex
int_0^(2pi) x^2/3-sin(x) dx
What is
(8pi^3)/9
If F'(x)=f(x) and f(x) is continuous and differentiable on the interval,
int_a^b f(x) dx=F(b)-F(a)
What is the Fundamental Theorem of Calculus?
When f'(x) changes from (+) to (-) at x=c
What is a local max
int_a^b sqrt(x'(t)^2+y'(t)^2) dt
What is arc length of a parametric curve?
The derivative of ln(x)
What is 1/x
The letter you add after finding the integral (you may have to solve for it)
What is C
In an alternating series, where the error bound is given by the absolute value of the first omitted term of the series
What is the Alternating Series Error Estimation Theorem
When f'(x) changes from (-) to (+)
What is a local min
Something implied by differentiability
What is continuity
The derivative of sec(x)
int sqrt(x)(x+2) dx
What is
2/5 x^(5/2) + 4/3 x^(3/2) +C
When a function f(x) is continuous on a closed interval [a,b], then f(x) takes on all values between f(a) and f(b)
What is Intermediate Value Theorem
Critical Points and Endpoints
What are Candidates (for Absolute Min/Max)
Maclaurin Series of e^x, sin(x), cos(x)
What is
e^x= sum_(n=0)^(infty) x^n/(n!),
sin(x)=sum_(n=0)^(infty) ((-1)^n x^(2n+1))/((2n+1)!),
cos(x)=sum_(n=0)^(infty) ((-1)^n x^(2n))/((2n)!)
The derivative of velocity
What is acceleration
The integral of
int x cos(x) dx
What is
xsin(x)+cos(x)+C
|f(x)-P_n(x)| \le |(max_(a \le x \le b) f^((n+1))(x))/((n+1)!) (x-a)^(n+1)|
What is the Taylor Error Theorem or the Lagrange Error Bound?
When f'(c) = 0 and f"(c) > 0
What is a local min
The Maclaurin series 1/(1-x
What is 1 + x + x2 + x3 + ... or
sum_(n=0)^(infty) x^n
The derivative of cos(2x+5)
What is −2sin(2x+5)
int e^x/(1+e^(2x)) dx
arctan(e^x)+C?
For the Mean Value Theorem to apply, what must be true of the function f(x)?
What is continuous and differentiable?
When f'(c) = 0 and f"(c) < 0
What is a local max
The technique of integration that requires you to factor the denominator
What is partial fraction?