Chapter 14: Q. 11 (page 889)

True or False If f is continuous at c, then $\lim_{x \to c^{+}} f (x) = f (c)$ .

Short Answer

Expert verified

The answer is True.

Step by step solution

Step. 1 Continuous function

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

Step. 2 Solution

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

$\lim_{x \to c} f (x) = f (c),$

or,

$L H L = R H L = f (c)$ ,

or,

$\lim_{x \to c^{-}} f (x) = \lim_{x \to c^{+}} f (x) = f (c)$ .

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

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True or False If f is continuous at c, then $\lim_{x \to c^{+}} f (x) = f (c)$ .

Short Answer

Step by step solution

Step. 1 Continuous function

Step. 2 Solution

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True or False If f is continuous at c, then $\lim_{x \to c^{+}} f (x) = f (c)$ .