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Grade 11Algebra

Lim[ (a+x)²sin (a+x)-a2sina]/x
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ashu

12 Years agoGrade 11

2 Answers

Arun Kumar

Approved Tutor Answer12 Years ago

Hi

$\\\lim_{x \to 0} [(a+x)^2sin(a+x)-a^2sina]/x \\form\, of \,0/0 \\=\lim_{x \to 0}$\left(\left(a+x\right)\left(a\cos \left(x+a\right)+x\cos \left(x+a\right)+2\sin \left(x+a\right)\right)\right)$ \\=$\left(a+\lim _{x\to \:0}\left(x\right)\right)$$\left(\lim _{x\to \:0}\left(a\cos \left(x+a\right)\right)+\lim _{x\to \:0}\left(x\cos \left(x+a\right)\right)+\lim _{x\to \:0}\left(2\sin \left(x+a\right)\right)\right)$ \\=$\left(a+0\right)\left(a\cos \left(a\right)+0+2\sin \left(a\right)\right)$ \\=$=a\left(2\sin \left(a\right)+a\cos \left(a\right)\right)$$

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

ashu

12 Years ago

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