JAMIA 2025 — Mathematics PYQ

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Question

JAMIA 2025 — Mathematics PYQ

JAMIA | Mathematics | 2025

$lim_{(x \to 0)} \frac{s i n x}{x} is:$

Choose the correct answer:

Explanation

Mathematical Solution:

Given Equation :

\lim_{x \to 0} \frac{\sin x}{x}

Jab hum $x = 0$ rakhte hain, toh hamein $\frac{0}{0}$ form milti hai, jo ki ek indeterminate form hai. Isse solve karne ke liye hum L'Hôpital's Rule ka upyog kar sakte hain:

\lim_{x \to 0} \frac{\sin x}{x} = \lim_{x \to 0} \frac{\frac{d}{dx}(\sin x)}{\frac{d}{dx}(x)}

Ab derivatives nikalne par:

\lim_{x \to 0} \frac{\cos x}{1}

Ab $x = 0$ ki value rakhne par:

\cos(0) = 1

Final Answer:

\lim_{x \to 0} \frac{\sin x}{x} = 1