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Find the linearization L(x) of the function f(x) = ln(1 + x) 0 votesFind the linearization L(x) of the attribute f(x) = ln(1 + x) at a = 0 and use it to approximate the numbers ln 1.2 and also ln 1.01. Compare the estimates from the direct approximation through the worths given by a calculator. Which among the 2 estimates is more exact, the estimation of ln 1.2 or the estimation of ln 1.01?linear-approximationaskedMar 15, 2015in CALCULUSby anonymous
Please log in or register to include a comment. Please log in or register to answer this question. 2 Answers 0 votes

Tip 1:

The feature is

*
.

You are watching: Find the linearization l(x) of the function at a

The linear approximation of a function is

*
.

Find the derivative of the function at

*
.

*

Now put

*
in
*
.

*

Tip 2:

*

*

Now find thelinear approximation at

*
.

*

So the linearapproximationat

*
is
*
.

answeredMar 20, 2015by yamin_mathMentor Please log in or register to include a comment. 0 votes

Contd...

Step 3:

Now usage the linear approximation to discover the

*
and
*
.

Recreate

*
.

Now compare it via the function

*
.

Here

*
.

Now approximate for

*
.

*

Tip 4:

Rewrite

*
.

Now compare it with the function

*
.

Here

*
.

Now approximate for

*
.

*

Step 5:

Now calculate

*
and
*
using calculator.

*

*

The second approximation is significantly better, because itis substantially closer to

*
than
*
.

Solution:

(1) The straight approximation is

*
.

(2)

*
.

(3)

*
.

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(4) The second approximation is even more accurate.

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