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Question 11 Mark
Show that function $f(x)=x^2, x=0$ is continuous.
Answer
Given function is defined at $x=0$ and the value of this is zero.$
\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} x^2=0
$
Thus $\quad \lim _{x \rightarrow 0} f(x)=f(x)=0=f(0)$
hence $f$ is continuous at $x=0$.
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Question 21 Mark
Show that function $F ( x )=\frac{1}{(x-a)},$ is discontinuous at $x=a$.
Answer
In $F(x)=\frac{1}{x-a}$ Put  $x=a$
$F(a)=\frac{1}{a-a}=\frac{1}{0}=$  not define 
hence it is not define at $x=a,$ so it is continuous.
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Question 31 Mark
If $f(x)=x \sin x$ then find $f^{\prime}\left(\frac{\pi}{2}\right)$.
Answer
$
\begin{aligned}
f^{\prime}(x) & =x \cos x+\sin x \\
f^{\prime}\left(\frac{\pi}{2}\right) & =\frac{\pi}{2} \cos \frac{\pi}{2}+\sin \frac{\pi}{2}=\frac{\pi}{2} \times 0+1 \\
& =1
\end{aligned}
$
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1 Marks Question - MATHS STD 12 Science Questions - Vidyadip