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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

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 .

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.