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Chapter 1: Q. 2 (page 86)

construct

construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) The graph of a function f for which f(2)does not exist but limx鈫�2f(x)does exist.

(b) The graph of a function f for which f(2)exists and limx鈫�2f(x)exists, but the two are not equal.

(c) The graph of a function f for which neither f(2)nor

limx鈫�2f(x)exist.

Short Answer

Expert verified

(a)f(x)=1x-2

(b)f(x)=x2.

(c)f(x)=1x2-22.

Step by step solution

01

Step 1. Given information.

(a) f(2)does not exist but limx鈫�2f(x)exists.

(b) f(2)and limx鈫�2f(x)both exist but they are not equal.

(c)f(2)&limx鈫�2f(x)both does not exists.

02

Step 2. Part (a)

Consider a function f(x)=1x-2.

here f(2)is undefined and does not exists but limx鈫�21x-2exists.

03

Step 3. Part (b)

Consider a function f(x)=x2.

here f(2)=4exists and limx鈫�2x2is also exists but they are not the same.

04

Step 4. Part(c)

Consider a function f(x)=1x2-22.

Here neitherf(2)exists norlimx鈫�21x2-22exists.

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