GATE CSE 1995 | Question: 7(B)

Question

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

Answer 1

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

$\qquad =1.$

Comments

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

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

 

Put x=0

Only 1 will remain

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 Sachin Mittal 1 I could not understand why u said we cant apply L Hospital's Rule. Please explain a bit more

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https://math.stackexchange.com/a/75151/545704