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

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

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hello Student,

\\Limit = lim(x\rightarrow 0)\frac{x-sinx.cosx}{x^{3}} \\Limit = lim(x\rightarrow 0)\frac{x-\frac{sin2x}{2}}{x^{3}} \\Limit = lim(x\rightarrow 0)\frac{1-cos2x}{3x^{2}} \\Limit = lim(x\rightarrow 0)\frac{2sin2x}{6x} \\Limit = \frac{2}{3}lim(x\rightarrow 0)\frac{sin2x}{2x} = \frac{2}{3}
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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