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using L hospital rule lim x=0 x-sinxcosx/x3

using L hospital rule lim x=0 x-sinxcosx/x3

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
L = lim(x\rightarrow 0)\frac{x-sinx.cosx}{x^{3}}
L = lim(x\rightarrow 0)\frac{x-\frac{sin2x}{2}}{x^{3}}
L = lim(x\rightarrow 0)\frac{1-cos2x}{3x^{2}}
L = lim(x\rightarrow 0)\frac{2sin2x}{6x}
L = \frac{2}{3}lim(x\rightarrow 0)\frac{sin2x}{2x} = \frac{2}{3}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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