Advanced Integration
Which integration technique should you use?
int (x/(x^2-1))dx
U-sub
What is the function for this series?
1-2x+4x^2-8x^3...
1/(1+2x)
Evaluate
\sum_{n=1}^{\infty} (-1)^(n+1)/3^n
1/12
Using Euler's method how many steps would you need to approximate f(1.57) using steps of 0.03 with initial condition (1,1)?
19
The number of teeth and adult has
32
Which integration technique should you use?
int (x^2*e^(2x))dx
Integration by parts
Find the simplified third-order Taylor polynomial for:
xcos(3x)
x - (9x^3)/2
Find the radius of convergence:
\sum_{n=1}^{\infty} x^n/(5^(n+1))
-5<x<5
Find the 4th order taylor polynomial for:
int_1^t (ln(1+x))dx
x^2/2 - x^3/6 + x^4/12
In what city do the Simpsons live?
Springfield
Which integration technique should you use?
int (1/(4x^2-81))dx
Partial Fraction Expansion
What is this series equivalent to?
pi/2 - (pi/2)^3/(3!) + (pi/2)^5/(5!)...
1
Does the series converge absolutely, converge conditionally, or diverge?
\sum_{n=1}^{\infty} (-1)^n * root{}[n] /(n^2)
Converges absolutely
Write the integral for the length of xln(x) from x =1 to x = 2.
int_1^2 (root{}[1+(ln(x)+1)^2]dx
What does the acronym W.H.O stand for?
World Health Organization
Which integration technique should you use?
int arctan(x)dx
Integration by parts
What is the coefficient of the x^12 term of
f(x) = e^(x^3)
1/24
Does the series converge absolutely, converge conditionally, or diverge?
\sum_{n=1}^{\infty} (-1)^n * (n^3 +3n^2 + 1)/(4n^4+n^3+1)
Converges conditionally
The first 3 terms of this series are used to approximate the sum of the series, what is the simplified error bound?
\sum_{n=1}^{\infty} (-1)^n * root{}[n] /(n^2)
1/8
Name 3 of the 7 ancient wonders of the world.
Pyramid of Giza
Lighthouse of Alexandria
Hanging Gardens of Babylon
Mausoleum of Halercanasus
Statue of Zeus at Olympia
Colossus of Rhodes
Temple of Artemis
int_1^\infty (2/(x^3))dx
1
Find the Lagrange error bound for a third-order approximation of f on the interval -1<x<1
f(x)=sin(2x)
2/3
Find the radius of convergence:
\sum_{n=1}^{\infty} (4^n * (2x-3)^n)/(n)
1/8
Find the interval of convergence:
\sum_{n=1}^{\infty} (x-3)^n/(2^n * n)
1<=x<5
These are the four countries that make up the United Kingdom
England, Wales, Northern Ireland, Scotland