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  • If <img alt="\lim _{x \rightarrow 0} \frac{\sin 2 x-a \sin x}{x^3}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim%20_%7Bx%20%5Crightarrow%200%7D%20%5Cfrac%7B%5Csin%202%20x-a%20%5

If \lim _{x \rightarrow 0} \frac{\sin 2 x-a \sin x}{x^3} is limit, then the value of a and the limit are respectively

Option: 1

2,-1


Option: 2

-1,1


Option: 3

2,1


Option: 4

-2,-1


Answers (1)

best_answer

\\\lim _{x \rightarrow 0} \frac{2 x-\frac{(2 x)^3}{3 !}+\ldots-a\left(x-\frac{x^3}{3 !}+\ldots\right)}{\lim _{x \rightarrow 0} \frac{x(2-a)+x^3\left(\frac{a}{6}-\frac{8}{6}\right)}{x^3}}\\ \\\\\text{for limit} 2-a=0, a=2\\ \\\\\frac{a}{6}-\frac{8}{6}=\frac{2-8}{6}=\frac{-6}{6}=-1

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