Integrate THIS
To Infinity..and Beyond!
Silly Series
Serious Series
Pretty Pictures
100
This is the integral of 1/(x*(ln(x))^3) dx packet 3, #5
What is -1/(2*ln(x)^2) + C
100
The limit x--> infinity of ln(x^2 +1) - ln(x + 2) quiz 3, # 5
What is infinty (or diverges)
100
This is the long term behavior of the series for tan-inverse of (n/2). E tan-1(n/2) packet 2, #1
What is diverges by the divergence test.
100
This is the Maclaurin series representation and radius for 1 / (1-x)
What is E x^n. n from 0 to infinity. Radius = 1
100
This is the graph of r = -3sin(theta).
What is a circle on y-axis with diameter of 3
200
This is the integral of 1/(x+1)(x-1) dx packet 3, #10
What is 1/2[-ln(x+1) + ln(x-1)]
200
Let f(x) = 2sin(x). Find f-inverse prime of 1.... (f^-1)'(1). quiz 1, #2
What is 1/sqrt(3)
200
This is the long term behavior of the series E cos(n pi) / (n+2).
What is converges by alternating series test
200
This is the interval of convergence for the power series E (x-3)^n / (n* 2^n) quiz 4, # 1
What is 2, and the series is centered at a = 3
200
This is the graph of r = sin(2*theta).
What is a flower with 4 loops, one in each quadrant
300
This is the integral of tan(x)sec(x)^2 dx packet 3, #9
What is 1/2 tan(x)^2) + C
300
This is the limit as x --> infinity of (1 + 8/x)^x. packet 3, #26
What is e^8
300
This is the number of terms needed to get error < 10^-8 for the series E (-1)^n+1 / n^4. written homework 6, #2
What is 99
300
Evaluate the integral x^2 / (1+x^2) dx as a power series centered at a = 0. Quiz 4, #2
What is C + E (-1)^n (x^(2n+3)) / (2n+3). n 0 to infinity
300
This is the slope of the curve r = sin(2*theta). packet 1, #2
What is sin(2theta)cos(theta)+2cos(2theta)sin(theta) / (-sin(2theta)sin(theta)+cos(theta)2cos(2theta).
400
This is the integral 1/sqrt(25-9x^2) dx packet 3, #14
What is 1/3 sin^-1(3x/5) + C
400
If f(x) = x^(ln x), this is the equation for f'(x). quiz 1, # 7
What is y'=(2 * x^(ln x) * ln x)/x
400
This is the long term behavior for the series E (2n+1)! / (n!)^2. packet 2, #12
What is diverges by ratio test.
400
This is the 3rd degree Taylor polynomial for f(x) = 1/x centered around x = 2. quiz 4, #8
What is 1/2 - 1/4 (x-2) + 1/8 (x-2)^2 - 1/16 (x-2)^3.
400
This is the area enclosed by the curve r = sin(2*theta). packet 1, #2
What is pi/2
500
This is the integral of e^x * cos(x) dx packet 3, #19
What is 1/2 e^x (cos(x)-sin(x) + C
500
This is where the sequence (2^n + (-1)^n)/ 3^n converges as n --> infinity. quiz 3, #6
What is 0
500
Does the series E (-1)^n / sqrt(2n+1) diverge, absolutely converge, or conditionally converge? packet 2, # 15
What is conditionally converge by alternating series test.
500
This is the power series expansion of the integral of cos(x^2)-1 / x^4 dx centered at a = 0. packet 2, #21
What is E (-1)^n x^(4n-3) / (2n!)(4n-3) n from 1 to inf
500
This is the Cartesian equation for the curve defined by x(t) = cos(t)^2 y(t) = 1-sin(t). Find arc-length if have time. packet 1, #1
What is x + (1-y)^2 = 1 acr length = integral from 0 to pi/2 sqrt[(4cos(theta)^2 sin(theta)^2) + cos(theta)^2]
M
e
n
u