AP EAMCET · Maths · Limits
If \(f(x)=\frac{5 x \cdot \operatorname{cosec}(\sqrt{x})-1}{(x-2) \operatorname{cosec}(\sqrt{x})}\), then \(\lim _{x \rightarrow \infty} f\left(x^2\right)=\)
- A 1
- B -1
- C 5
- D -5
Answer & Solution
Correct Answer
(C) 5
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } f(x)=\frac{5 x \operatorname{cosec}(\sqrt{x})-1}{(x-2) \operatorname{cosec}(\sqrt{x})} \\ & f\left(x^2\right)=\frac{5 x^2 \operatorname{cosec} x-1}{\left(x^2-2\right) \operatorname{cosec} x}=\frac{5 x^2}{x^2-2}-\frac{\sin x}{x^2-2} \\ & \lim _{x…
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