Question

Asked Oct 16, 2019

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Determine how many terms are needed to compute:

ln 1.1 with error less than (1/2)×10^(−8) using alternating series theorem and Taylor series of ln(1 + x) about x = 0.

Step 1

From the given information it is needed to calculate the number of terms for ln(1.1) with error less than 1/2×10^{-8} by using the alternative series theorem and taylor series expansion of ln(1+x) about x=0.

So, use the form of remainder in taylor series. The lagrange form for the remainder on the closed interval from a to x is:

Step 2

Now, it is required to calculate the value of k such that the remainder R_{k}(1.1)

for the k^{th} order taylor series for ln(x) about x=0 is less than 1/2×10^{-8}

Step 3

So, to calculate the valu...

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