IGNOU BMTC 102 2026 - निम्नलिखित सीमा ज्ञात कीजिए : (i) (ii)

Question

निम्नलिखित सीमा ज्ञात कीजिए :
(i) $\quad \lim_{x \to +\infty} \left( \frac{x^2}{8x^2 - 3} \right)^{1/3}$
(ii) $\quad \lim_{x \to 0^+} (\sin x)^{\sin x}$

09 Jan 2026

Answer :

Word Count : 174

(i) (\displaystyle \lim_{x \to +\infty} \left( \frac{x^2}{8x^2 - 3} \right)^{1/3}) सबसे पहले अन्दर के अनुपात पर ध्यान दें: [ \frac{x^2}{8x^2 - 3} = \frac{x^2}{x^2(8 - 3/x^2)} = \frac{1}{8 - 3/x^2} ] जब (x \to +\infty), तो (3/x^2 \to 0)। अतः: [ \frac{x^2}{8x^2 - 3} \to \frac{1}{8} ] अब, पूरा सीमा: [ \left( \frac{x^2}{8x^2 - 3} \right)^{1/3} \to \left( \frac{1}{8} \right)^{1/3} =

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