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.) 1/((1 + 9x)^4) ≈ 1 − 36x

Part 1)

See Below.

Part 2)

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

We want to verify that the expression:

Is the linear approximation for the function:

At x = 0.

So, find f'(x). We can use the chain rule:

Simplify. Hence:

Then the slope of the linear approximation at x = 0 will be:

And the value of the function at x = 0 is:

Thus, the linear approximation will be:

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

By definition:

Therefore:

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

70

step-by-step explanation: