Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

2nd Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781133112280

Chapter C, Problem 1E

(a)

To determine

**To show:** The inequality

Expert Solution

**Definition used:**

The natural logarithmic function is the function defined by

If *t* = 1 to *t* = *x.*

**Calculation:**

The given inequality is

Here,

By using the above mentioned definition, *t* = 1 to *t* = 1.5*.*

Use online graphing calculator, graph of the curve

From Figure 1, it is observed that the area is larger than the area of rectangle *BCDE* and smaller than the area of trapezoid *ABCD.*

The area of the rectangle *BCDE* is calculated as follows.

The area of the trapezoid *ABCD* is calculated as follows.

It is known that the value of

The decimal value of the fraction

By comparing the above values with

Hence proved.

(b)

To determine

**To show:** The function

Expert Solution

The estimated value of

**Definition used:**

*Midpoint Rule:*

Midpoint rule can be defined as

Where,

*Natural logarithmic:*

The natural logarithmic function is the function defined by

**Calculation:**

It is known that the equation of the curve is

Here,

From definition of natural logarithmic, the function

Here,

Find

Estimate the value of

Further simplification,

Therefore, the estimated value of

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!