# Taylor's inequality,math homework help

**Question description**

Taylor series of ln(1-x)

Find the smallest value of n such that Taylor's inequality guarantees that

|Tn(x)âln(1âx)|<0.01

for all x in the interval

(-.5, .5)

## Tutor Answer

This is the solution using the Lagrange remainder and its straightforward estimate. Tell me if this is not what you want.

The Taylor series centered at đĽ = 0 for the function đ(đĽ) = ln(1 â đĽ) is

â

đ(đĽ) = â â

đ=1

đĽđ

.

đ

The remainder of the Taylor đ-th partial sum may be expressed as

đ(đĽ) â đđ (đĽ) =

đ (đ+1) (đ) đ+1

đĽ

,

(đ + 1)!

wh...

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