Let f (x) be continuous on [a, b]. If F(x) is any antiderivative of f(x), then
the integral of f(x)dx = F(b) - F(a)
fundamental theorem of calculus
200
∫ (x^3-x-1)/(x^2) dx
(x^2)/2-lnx+(1/x)+c
200
What is the derivative of y=ln(secx+tanx)?
sec(x)
200
What is the sum of the geometric series 2-1+(1/2)-(1/4)+(1/8)....
4/3
200
Find the limit as x approaches infinity of (3x+5)/(7x-2).
3/7
200
Approximate the area under the curve using rectangles or trapezoids.
Reimann sum
300
∫ sinθcosθ dθ
-.25cos2θ+c
300
What is the derivative of tan3x?
3(sec3x)^2
300
Does the series ((-1)^n)/(n^1/2) converge or diverge?
It converges
300
Find the limit as x approaches 3 of (x-3)/(x+2).
0
300
The value a function approaches as the variable within that function gets nearer and nearer to a particular value.
limit
400
∫ xcosx dx
xsinx+cosx+c
400
Find dy/dx when x=1/(1-t) and y=1-ln(1-t)
(1-t)^2/t
400
What is the fifth degree Taylor polynomial for sin x
x-(x^3/6)+(x^5/120)
400
Find the limit as x approaches 0 of (4xcosx)/(sinx)
4
400
f'(x)=the limit as h approaches 0 of (f(x+h)-f(x))/h
derivative
500
∫ e^2lnu du
(u^3)/3 +c
500
Find dy/dx when x=(cosθ)^3 and y=(sinθ)^3
-tan(θ)
500
For what values of x does the series n!(x-3)^n converge
x=3
500
Find the limit as x approaches -4 of (x^2+6x+8)/(x+4).
-2
500
If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b), then there is at least one number x in the closed interval such that f(x)=c.