Power Series Flashcards
What is the interval of convergence for 1/(1-x)
(-1, 1)
What is the interval of convergence for ex
(-∞, ∞)
What is the interval of convergence for sin(x)
(-∞, ∞)
What is the interval of convergence for cos(x)
(-∞, ∞)
What is the interval of convergence for tan-1(x)
[-1, 1]
What is the interval of convergence for ln(1+x)
(-1, 1]
What is the sigma notation for 1/(1-x)
Σ∞n=0(xn)
What is the sigma notation for ex
Σ∞n=0(xn/n!)
What is the sigma notation for sin(x)
Σ∞n=0((-1)nx2n+1/(2n+1)!)
What is the sigma notation for cos(x)
Σ∞n=0((-1)nx2n/(2n)!)
What is the sigma notation for tan-1(x)
Σ∞n=0((-1)nx2n+1/(2n+1))
What is the sigma notation for ln(1+x)
Σ∞n=1((-1)n+1xn/n)
What are the first four terms of the maclaurin series for 1/(1-x)
1 + x + x2 + x3
What are the first four terms of the maclaurin series for ex
1 + x/1! + x2/2! + x3/3!
What are the first four terms of the maclaurin series for sin(x)
x - x3/3! + x5/5! - x7/7!
What are the first four terms of the maclaurin series for cos(x)
1 - x2/2! + x4/4! - x6/6!
What are the first four terms of the maclaurin series for tan-1(x)
x - x3/3 + x5/5 - x7/7
What are the first four terms of the maclaurin series for ln(1+x)
x - x2/2 + x3/3 - x4/4
What series can be written as this using sigma notation:
Σ∞n=0(xn)
1/(1-x)
What series can be written as this using sigma notation:
Σ∞n=0(xn/n!)
ex
What series can be written as this using sigma notation:
Σ∞n=0((-1)nx2n+1/(2n+1)!)
sin(x)
What series can be written as this using sigma notation:
Σ∞n=0((-1)nx2n/(2n)!)
cos(x)
What series can be written as this using sigma notation:
Σ∞n=0((-1)nx2n+1/(2n+1))
tan-1(x)
What series can be written as this using sigma notation:
Σ∞n=0((-1)n+1xn/n)
ln(1+x)
delete this card later pls
idk
What maclaurin series starts with these four terms:
1 + x + x2 + x3
1/(1-x)
What maclaurin series starts with these four terms:
1 + x/1! + x2/2! + x3/3!
ex
What maclaurin series starts with these four terms:
1 + x/1! + x2/2! + x3/3!
ex
What maclaurin series starts with these four terms:
x - x3/3! + x5/5! - x7/7!
sin(x)
What maclaurin series starts with these four terms:
x - x3/3! + x5/5! - x7/7!
sin(x)
What maclaurin series starts with these four terms:
1 - x2/2! + x4/4! - x6/6!
cos(x)
What maclaurin series starts with these four terms:
1 - x2/2! + x4/4! - x6/6!
cos(x)
What maclaurin series starts with these four terms:
x - x3/3 + x5/5 - x7/7
tan-1(x)
What maclaurin series starts with these four terms:
x - x3/3 + x5/5 - x7/7
tan-1(x)
What maclaurin series starts with these four terms:
x - x2/2 + x3/3 - x4/4
ln(1+x)
Which series have this interval of convergence:
(-1, 1)
1/(1-x)
Which series have this interval of convergence:
(-∞, ∞)
ex, sin(x), cos(x)
Which series have this interval of convergence:
[-1, 1]
tan-1(x)
Which series have this interval of convergence:
(-1, 1]
ln(1+x)
