Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Correct: Your answer is correct. Use it to approximate the numbers 3 0.95 and 3 1.1 . (Round your answers to three decimal places.)

2.835

3.330

Step-by-step explanation:

Let the linear approximation be L(x) at a = 0. This is given by

is the derivative of . To find this, we use the form

If , then

By doing this and applying chain rule for the power (which is a function of x), we have

Then

Also

Hence

For , and

Using this in ,

For , and

Using this in ,

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