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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 5.1, Problem 4E

**(a)**

To determine

**To Analyze:**

Whether the estimate is an underestimate or an overestimate using right endpoints.

Expert Solution

The estimate is an overestimate for the function

**Given information:**

The curve function is

The region lies between

The number of rectangles

Draw the graph for the function

Draw four approximating rectangles using right end points for the function

The expression to find the lower estimate of areas of *n* rectangles

Here, the right endpoint height of the first rectangle is *n*^{th} rectangle is

Find the width

Here, the upper limit is *b*, the lower limit is *a*, and the number of rectangles is *n*.

Substitute *b*, 0 for *a*, and 4 for *n* in Equation (2).

Refer Figure (2).

Take the right endpoint height of the first rectangle

Substitute 4 for *n*, 0.38for

Refer Figure (2).

The function curve as

Hence,

(b)

To determine

**To Analyze:**

Whether the estimate is an underestimate or an overestimate using right endpoints.

Expert Solution

The estimate is an underestimate for the function

Draw four approximating rectangles using left end points for the function

The expression to find the upper estimate of areas of 4 rectangles

Here, the lower estimate using right endpoints for

Refer Figure (3).

Take the left endpoint height of the uppermost left rectangle

Substitute 1.182 for

Refer Figure (3).

The function curve as

Hence,