IGNOU BMTC 102 2026 - यदि तो a और b के मान ज्ञात कीजिए।

Question

यदि $\lim_{x \to 0} \frac{x(1 + a \cos x) - b \sin x}{x^3} = 1$ तो a और b के मान ज्ञात कीजिए।

09 Jan 2026

Answer :

Word Count : 362

सीधे समाधान शुरू करते हैं। हमें दिया गया है: [ \lim_{x \to 0} \frac{x(1 + a \cos x) - b \sin x}{x^3} = 1 ] चरण 1: नियमानुसार टेलर श्रृंखला विस्तार करें * (\cos x = 1 - \frac{x^2}{2} + O(x^4)) * (\sin x = x - \frac{x^3}{6} + O(x^5)) इन्हें भिन्न में प्रतिस्थापित करें: [ x(1 + a \cos x) = x \big(1 + a (1 - \frac{x^2}{2} + \cdots) \big) = x(1 + a - \frac{a x^2}{2} + \cdots) = x(1+a) - \frac{a x^3}{2} + \cdots ] [ b \sin x = b \left(x - \frac{x^3}{6} + \cdots \right) = b x - \frac{b x^3}{6} + \cdots ] तो भिन्न बनेगा: [ x(1 + a \cos x) - b \sin x = (x(1+a) - b x) + \left(-\frac{a

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