The value of the number of interval ( n ).

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 5.1, Problem 24E
To determine

To find: The value of the number of interval (n).

Expert Solution

The value of n is 377,340_.

Explanation of Solution

Given information:

The curve function is f(x)=y=ex.

The upper limit (b) is 3 and the lower limit (a) is 1.

The relation given is RnA<0.0001 (1)

The relation to find the value of n is shown below:

RnA<ban[f(b)f(a)] (2)

Here, the upper sum is Rn, the area is A, the lower limit is a, the upper limit is b, and the difference in curve function value is [f(b)f(a)].

Substitute 3 for b and 1 for a in Equation (2).

RnA=31n[f(3)f(1)]=31n[e3e1]=2n(17.367)=37.734n

Substitute 37.734n for (RnA) in Equation (1).

37.734n<0.0001n>37.7340.0001=377340

Therefore, the value of n is 377340_.

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