5 b) Examine the following functions for continuity. 

f (x) = \frac{1}{x-5} , x \neq 5 

Answers (1)

Given function is
f(x ) = \frac{1}{x-5}
For every real number  k , k \neq 5
We get,
f(k) = \frac{1}{k-5}\\ \lim_{x\rightarrow k}f(x ) = \frac{1}{k-5}\\ \lim_{x\rightarrow k}f(x ) = f(k)
Hence, function  f(x ) = \frac{1}{x-5} continuous for every real value of x, x \neq 5

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