Question

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

• A. 0
• B. 1
• C. -1
• D.

Answer 1

The correct option is B

1

We have, $\underset{x\to 0}{lim}\frac{tanx}{x}$

While evaluating the value of given limit we can use expansion of tan x

We know,

$tanx=x+\frac{x^3}{3}+\frac{2x^5}{15}+\frac{17}{315}{x}^7+........$

Substituting the expansion of tan x in the numerator of limits

$\underset{x\to 0}{lim}\frac{x+\frac{x^3}{3}+\frac{2x^5}{15}+\frac{17}{315}{x}^7+........}{x}$

$\underset{x\to 0}{lim}1+\frac{x^3}{3}+\frac{2}{15}{x}^4+\frac{17}{315}{x}^6+........$

$=1$

Option B is correct