(a).

The series is .

Find the sum of the first ten terms of the series.

The sum of the first ten terms is .

Estimate the error using Remainder estimate for the integral test.

Substitute .

The error is which is not greater than .

The error is not more than .

(b).

Equation : .

Here , since and .

Substiute the values.

Consider .

.

Substitute , and .

Therefore

.

Consider as the average of the upper and the lower bounds , we have

and with error .

(c).

The value of and error .

From the result of exercise 35, .

Difference with Eulers exact value :.

The value is within the range of error calulated for the estimate.

(d).

The function , since .

Estimate the error using Remainder estimate for the integral test.

the error is   is no more than  .

Therefore , we need to find the value of so that .

The value of .

Since has to be an integer , so is atleast  , i.e., .

(a)The error is not more than .

(b) error .

(c) .

(d) .