# A small selection of Calculus questions

1. Give the value of c in the interval [0,3] that satisfies the conclusion of the mean value theorem for -2*sqrt(x)-2

2. Use differentials to estimate the fourth root of 80.

3. Use differentials to estimate the sine of 44 degrees.

4. Use one iteration of Newton's method to approximate a solution to x^3+x-352=0 with initial guess x=7.

The attached file contains these questions written with correct mathematical notation.

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#### Solution Preview

Solution is attached.

1. Give the value of c in the interval [0,3] that satisfies the conclusion of the mean value theorem for

The mean value theorem tells us that there exists some c in the interval for which

So we have to solve

Rearranging

2. Use differentials to estimate the fourth ...

#### Solution Summary

The solution comprises approximately 1 1/4 pages in Word with equations written in Mathtype. All steps are explained.