Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) 4 1 + 2x ≈ 1 + 1 2 x

x ∈ [-0.369, 0.678]

Step-by-step explanation:

To prove - ≈ 1 + x

As given , f(x) =

As we know that the linear approximation can be defined as :

L(x) = f(a) + f'(a)(x-a)             .........(1)

Now,

We have to show that at a = 0 , equation (1) satisfies

Now,

f(0) = = 1

Also,

f'(x) =

∴ we get

f'(x) =

⇒f'(0) =

Now, equation (1) becomes

L(x) = f(0) + f'(0)(x-0)

     = 1 + (x)

⇒ ≈ 1 + x

Hence verified.

Now,

| - (1 + x ) | ≤ 0.1

⇒ -0.36893 ≤ x ≤ 0.67766

⇒x ∈ [-0.369, 0.678]

yor answer is 7/6 times 5

step-by-step explanation: