lim_(x->0)(1 + sinx)/(cosx) =? 

প্রশ্ন: \( \lim_{x \to 0} \frac{1 + \sin x}{\cos x} = ? \)

সমাধান:

আমরা জানি, \( \lim_{x \to 0} \sin x = 0 \) এবং \( \lim_{x \to 0} \cos x = 1 \)।

সুতরাং,

\( \lim_{x \to 0} \frac{1 + \sin x}{\cos x} = \frac{1 + \lim_{x \to 0} \sin x}{\lim_{x \to 0} \cos x} \)

\( = \frac{1 + 0}{1} \)

\( = \frac{1}{1} \)

\( = 1 \)

অতএব, \( \lim_{x \to 0} \frac{1 + \sin x}{\cos x} = 1 \)। 🎉