Asked Oct 16, 2019

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. 


Expert Answer

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:


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k+1 (x-a), for some (k+1)! between a and x R,(x)= _

Step 2

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

for the kth order  taylor series for ln(x) about x=0 is less than 1/2×10-8


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(x-1) (x-1) i-1 and R (x) k 1-1

Step 3

So, to calculate the valu...


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1 < E, where e =-x10 2 and a 1.1 k so 1.1 -x10 k 1 2


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