Module 6 - Limit as <i>x</i> Approaches <i>a</i>

Module 6 - Answers

Lesson 1

Answer 1

6.1.1 The smaller tolerance for x, 0.13, will ensure that y is within 0.1 of 2 when x is close to 3.

Answer 2

6.1.2 To ensure that y is within 0.01 of 2, x should be within 0.0133 of 3.

Lesson 2

Answer 1

6.2.1 Find a positive number

so that

when

Answer 2

6.2.2

Answer 3

6.2.3 Solve

and

for

to obtain

and

. The correct tolerance is the minimum of the two values,

Answer 4

6.2.4 Given a positive number

find a positive number

that will ensure that

whenever

Self Test

Answer 1

The x-value should be within 0.0488088 of 1 to ensure that x² + 3 is within 0.1 of 4.

Answer 2

Find a positive number so that 4 - 0.1 < x² + 3 < 4 + 0.1 whenever . The x-value should be within 0.0488088 of 1

Answer 3