Question

lim x → 0 (1/x)^2sinx​

Answer 1

Answer: doesnt exits

.= lim x → 0 (1/x)^2sinx​=

Step-by-step explanation:

.= lim x → 0 (1/x)^2sinx​

.= lim x → 0 (1/x)sinx​.* lim x → 0 (1/x)

.=1. Indeterminate.  = Does not exit.

using Lhospital

.= lim x → 0 (1/x)^2sinx​= .

= lim x → 0 cos x/ 2x

doesnt exit !

Answer 2

Answer:

$\lim_{x \to 0} \frac{1}{x^{2}} sin x$ = ∞

Step-by-step explanation:

We need to find $\lim_{x \to 0} \frac{1}{x^{2}} sin x$

= > $\lim_{x \to 0} \frac{ sin x}{x^{2}}$

=> $\lim_{x \to 0} \frac{ sin x}{x} * \frac{1}{x}$

=>  $\lim_{x \to 0} (\frac{ sin x}{x} * \frac{1}{x})$

On separating the limits,

=> $\lim_{x \to 0} (\frac{ sin x}{x}) * \lim_{x \to 0}(\frac{1}{x})$

We know that $\lim_{x \to 0} \frac{ sin x}{x}$ = 1

=> 1 * $\lim_{x \to 0} \frac{1}{x}$

=>  $\lim_{x \to 0} \frac{1}{x}$

Applying the limit to the function.

=> $\frac{1}{0}$

=> ∞