   Chapter 5.1, Problem 24E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Determine a region whose area is equal to the given limit. Do not evaluate the limit. lim n → ∞ ∑ i = 1 n 3 n 1 + 3 i n

To determine

The region bounded by the area for the given limit.

Explanation

Given information:

The limit is limni=1n3n1+3in (1)

The expression for area under the graph is shown below:

A=limni=1nf(xi)Δx (2)

Here, the width of the interval is Δx and the curve function is f(xi)

Calculation:

The expression for width of the interval (Δx) is shown below:

Δx=ban (3)

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

Find the value of xi using the relation:

xi=a+iΔx (4)

Substitute a+iΔx for xi in Equation (2)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 