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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The point(s) at which the function $f$ given by
$f(x)=\begin{cases}
\dfrac{x}{|x|}, & x<0 \\
-1, & x\ge 0
\end{cases}$
is continuous is/are.
Solution
For $x<0$, $|x|=-x$ so $f(x)=\dfrac{x}{-x}=-1$ (constant) ⇒ continuous. For $x>0$, $f(x)=-1$ ⇒ continuous. At $x=0$: $\displaystyle \lim_{x\to0^-} f(x)=-1,\quad \lim_{x\to0^+} f(x)=-1,\quad f(0)=-1$ Hence $f$ is continuous at $x=0$. Therefore, $f$ is continuous for all real $x$.Online Test Series, Information About Examination,
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