lim _{x rightarrow 0} x^2 sin left(frac{pi}{x | vedclass

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(B) We use the Squeeze Theorem to evaluate the limit.We know that for all $x 
eq 0$,$-1 \leq \sin \left(\frac{\pi}{x}ight) \leq 1$.Multiplying the

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(B) We use the Squeeze Theorem to evaluate the limit.We know that for all $x 
eq 0$,$-1 \leq \sin \left(\frac{\pi}{x}ight) \leq 1$.Multiplying the inequality by $x^2$ (since $x^2 > 0$ for $x 
eq 0$),we get:$-x^2 \leq x^2 \sin \left(\frac{\pi}{x}ight) \leq x^2$.Now,taking the limit as $x ightarrow 0$ on all sides:$\lim _{x ightarrow 0} (-x^2) \leq \lim _{x ightarrow 0} x^2 \sin \left(\frac{\pi}{x}ight) \leq \lim _{x ightarrow 0} x^2$.Since $\lim _{x ightarrow 0} (-x^2) = 0$ and $\lim _{x ightarrow 0} x^2 = 0$,by the Squeeze Theorem:$\lim _{x ightarrow 0} x^2 \sin \left(\frac{\pi}{x}ight) = 0$.

List-$I$	List-$II$
$A$. Tranquilizers	$I$. Anti blood clotting
$B$. Aspirin	$II$. Salvarsan
$C$. Antibiotic	$III$. Antidepressant drugs
$D$. Antiseptic	$IV$. Soframicine

$\lim _{x \rightarrow 0} x^2 \sin \left(\frac{\pi}{x}\right)$ is equal to

Similar Questions

Match List-$I$ with List-$II$:

List-$I$ List-$II$

$A$. Tranquilizers $I$. Anti blood clotting

$B$. Aspirin $II$. Salvarsan

$C$. Antibiotic $III$. Antidepressant drugs

$D$. Antiseptic $IV$. Soframicine

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