Operations with Power Series
If f(x)=∑anxn and g(x)=∑bnxn, what is the series for f(x)+g(x)?
∑(an+bn)xn
What is the interval of convergence of the Maclaurin series of ex?
-∞<x<∞
General form of power series expansion of f(x) about x=c.
f(x)=∑an(x-c)n
What is the differentiation of ∑an(x-c)n?
∑nan(x-c)n-1
If f(x)=∑anxn, what is the series for f(kx).
∑anknxn
What is the third term of Maclaurin Series for ln(x)?
Maclaurin Series is Undefined or DNE
What is the power series of 1/1-x about 0?
∑xn where |x|<1
Intergrate ∑an(x-c)n
∑((an/n+1)(x-c)n+1)+C REMEMBER THE +C
For f(x)=∑anxn, express f(xN) as a power series.
f(xN)=∑anxnN
(-1)nxn is the general term of the Maclaurin Series of what function?
1/(1+x)
Is the Maclaurin series for ln(1+x) or sinx more accurate?
Sinx
What is the derivative of ∑annxn?
∑an(xn+n2xn-1)
If f(x)=∑anxn, what is the series for xmf(x)?
∑anxn+m
What is the elementary function of the binomial series?
f(x)=(x+1)k or (1+x)k
What is the power series representation for 1/(1-x)2?
∑nxn-1
If f(x)=∑an(x-e)n what is the intergral?
C+∑an(x-e)n+1/(n+1)
Given the two power‐series functions f(x)=∑anxn and g(x)=∑bnxn what is the series of f(x)g(x).
∑n=0∞(∑k=0∞akbn-k)xn
1. When the Lagrange Error bound and AST can be applied, which error bound test provides the more accurate error bound?
2. What is the inequality between the maximum error value that the Lagrange Error Bound provides and the one that the Alternating Series Error Bound provides?
Both parts 1 and 2 need to be answered correctly to get the points for this question!
1. AST
2. AST<=Lagrange Error
What is the general term of (1+x)a where a is a constant?
(a(a-1)...(a-n+1))/n!
Write the first three terms of the integral of f(x) if f(x)=∑an(x-e)n?
C+a0(x-e)+a1(x-e)2/2