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এই সীমার মান নির্ণয় করতে, প্রথমে ডিগ্রি পরিমাপকে রেডিয়ানে রূপান্তর করতে হবে। আমরা জানি যে, \(1^{ iny ext{o}} = \frac{\pi}{180}\) রেডিয়ান।

সুতরাং, \(2x^{ iny ext{o}} = 2x \times \frac{\pi}{180} = \frac{\pi x}{90}\) রেডিয়ান।

প্রশ্নটি যদি \(\lim_{x \rightarrow 0} \left ( \frac{\sin{2} x^{\tiny\text{o}}}{x} \right )\) হয় (যা প্রদত্ত অপশনগুলোর সাথে মিলে যায়), তাহলে সীমাটি হবে:

\( \lim_{x \rightarrow 0} \frac{\sin\left(\frac{\pi x}{90}\right)}{x} \)

এখন, আমরা এটিকে আদর্শ সীমা সূত্র \( \lim_{y \rightarrow 0} \frac{\sin y}{y} = 1 \) এর আকারে আনার চেষ্টা করব। এর জন্য ভগ্নাংশের লব এবং হরকে \( \frac{\pi}{90} \) দিয়ে গুণ করতে হবে:

\( = \lim_{x \rightarrow 0} \frac{\sin\left(\frac{\pi x}{90}\right)}{\frac{\pi x}{90}} \times \frac{\pi}{90} \)

যখন \(x \rightarrow 0\) হয়, তখন \( \frac{\pi x}{90} \rightarrow 0 \)।

অতএব,

\( \lim_{x \rightarrow 0} \frac{\sin\left(\frac{\pi x}{90}\right)}{\frac{\pi x}{90}} = 1 \)

সুতরাং, সীমার মান হবে:

\( 1 \times \frac{\pi}{90} = \frac{\pi}{90} \)

সঠিক উত্তরটি হলো

( lim_ x rightarrow 0 left ( frac sin 2 x ° x° right ) ) এর মান কোনটি?