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Is the function $f(x) = 5x-3$ continous at $x=0$?

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  • If $f$ is a real function on a subset of the real numbers and $c$ a point in the domain of $f$, then $f$ is continous at $c$ if $\lim\limits_{x\to c} f(x) = f(c)$.
Given $f(x) = 5x-3$.
At $x=0, \; \lim\limits_{x\to 0} f(x) = \lim\limits_{x\to 0} 5x-3 = 5 \times 0 - 3 = -3$
$f(0) = 5 \times 0 - 3 = -3$
Since $\lim\limits_{x\to 0} f(x) = f(0)$, $f(x)$ is continous at $x=0$.
answered Apr 4, 2013 by balaji.thirumalai

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