Find the taylor polynomial t1(x) for the function f(x)=ln(x) based at b=1.

The taylor polynomial for the function (f(x)=ln(x)) based at b=1 is (f(x) = x-1) and this can be determined by using the Taylor first degree approximation formula.

Given :

f(x) = ln(x)

The following steps can be used n order to determine the Taylor polynomial:

Step 1 - The Taylor approximation is given by:

Step 2 - Now, differentiate the given function f(x) = ln(x).

Step 3 - Now, substitute the value of (x = 1) in the above expression.

Step 3 - Now, the first degree Taylor approximation is given by:

Step 4 - Substitute the values of the known terms in the above expression.

Step 5 - Simplify the above expression.

f(x) = ln(1) + (x - 1)

f(x) = x - 1

So, the taylor polynomial for the function (f(x)=ln(x)) based at b=1 is (f(x) = x-1).

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