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Chapter 14: Q. 11 (page 889)

True or False If f is continuous at c, thenlimx鈫�c+f(x)=f(c).

Short Answer

Expert verified

The answer is True.

Step by step solution

01

Step. 1 Continuous function

A function is said to be continuous at a point x=c, if its limit at x=cexist and is equal to the absolute value of f(x)at c.

02

Step. 2 Solution

Let f(x)be continuous at x=c, then from above definition,

limx鈫�cf(x)=f(c),

or,

LHL=RHL=f(c),

or,

limx鈫�c-f(x)=limx鈫�c+f(x)=f(c).

So, from this equation it is clear that the above statement is true.

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