GATE (TF) Textile 2015 Question Paper Solution | GATE/2015/TF/13

Question 13 (Textile Engineering & Fibre Science)

The value of $\lim_{x\to 0} \frac{\sin x}{x}$ is __1__.

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$\lim_{x\to 0} \frac{\sin x}{x}$
As we know,
Sin x= $x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+..........$
$\lim_{x\to 0} \frac{x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+.........}{x}$
$\lim_{x\to 0}{1-\frac{x^2}{3!}+\frac{x^4}{5!}-\frac{x^6}{7!}+.........}$
By taking limit-
=1+0
=1(Ans)

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