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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