Question

Find the value of $\underset{x\to 0}{lim}\frac{sinx}{x}$

• A. 0
• B. 1
• C. -1
• D.

Answer 1

The correct option is B

1

We have Find the value of $\underset{x\to 0}{lim}\frac{sinx}{x}$

To evaluate the value of given limit,

we can yse the expression of $sinx=x-\frac{x^3}{3!}+\frac{x^5}{5!}-..........$

Substituting the expansion of sinx

in the numerator of the limit$\underset{x\to 0}{lim}\frac{x-\frac{x^3}{3!}+\frac{x^5}{5!}-.....}{x}$

$\underset{x\to 0}{lim}(1-\frac{x^2}{3!}+\frac{x^5}{5!}-.....)$

Putting x=0

$=1-0+0$

$=1$

Option B is correct