Calc BC Ch 8

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Taylor Polynomial

Exponent matches factorial

Find values of x for which the series converges

\-1 < x < 1 ( DIVERGES \[ CONVERGES

Maclaurin Series lnx

Maclaurin Series e^x

Maclaruin Series sinx

odd exponents/factorials

Maclaurin Series cosx

even exponents/factorials

nth term

n^x

nth term

≠ 0… diverge

geo

x^n

geo

|fraction| < 1… converge

|fraction| ≥ 1… diverge

p series

1/n^x

p series

exponent > 1… converge

exponent ≤ 1… diverge

ratio

n, x^n, and factorials… do fun a(n+1) reciprocal stuff!!

ratio

L < 1… converge

L > 1… diverge