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Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$

$\displaystyle \lim_{x\rightarrow 0}\frac{\sin x}{x} = \displaystyle \lim_{x\rightarrow 0}\frac{\cos x}{1}$ (Applying L'Hôpital's rule since 0/0 form)

$\qquad =1.$

Expand Sinx =x-(x^3)/3 ..

Sinx/x= 1-(X^2)/3....

Put x=0

Only 1 will remain

I could not understand why u said we cant apply L Hospital's Rule. Please explain a bit more

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