mathop {lim }limits_{x to pi /2} frac{tan 3x} | vedclass

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Question

(A) We need to evaluate the limit: $\mathop {\lim }\limits_{x 	o \pi /2} \frac{	an 3x}{x}$.As $x 	o \pi /2$,the numerator $	an 3x$ approaches $	a

Vedclass · Accepted Answer

$\infty $

Vedclass · Answer

(A) We need to evaluate the limit: $\mathop {\lim }\limits_{x 	o \pi /2} \frac{	an 3x}{x}$.As $x 	o \pi /2$,the numerator $	an 3x$ approaches $	an(3\pi / 2)$,which is undefined (tends to $\pm \infty$ depending on the direction).The denominator $x$ approaches $\pi / 2$.Since the numerator is undefined and the denominator is a finite non-zero value,the limit does not exist in the real number system and tends to $\infty$ in the context of extended real numbers.Therefore,the correct option is $A$.

$\mathop {\lim }\limits_{x \to \pi /2} \frac{\tan 3x}{x} = $

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