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Differential Calculus

Blazing goIITian

 Joined: 1 Apr 2012 Post: 381
19 May 2012 21:43:53 IST
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limit (conceptual)
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Differential Calculus

evalute  limx->0     [ln(1+(sin^2)*x)cot ln^2 (1+x)]   using LH rule          ans=1

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Joined: 23 Jan 2007
Posts: 7958
19 May 2012 22:22:17 IST
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$\lim_{x \to 0 }ln(1+sin^2x)cot(ln^2(1+x))$

$=\lim_{x \to 0 }\frac{ln(1+sin^2x)}{tan(ln^2(1+x))}$

$=\lim_{x \to 0 }\frac{sin^2x}{ln^2(1+x)}\; (since\; ln(1+x)\approx\ x; and\; sinx\approx x\; as\; x \to0)$

$=\lim_{x \to 0 }\frac{sin^2x}{x^2}\; (since\; ln(1+x)\approx\ x\; as\; x \to0)$

$=1$

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