Question

$\underset{x\to a}{lim}\frac{\log x-\log a}{\tan (x-a)}$=

• A. $\frac{1}{a}$
• B. $a$
• C. $0$
• D. $\frac{2}{a}$

Answer 1

Answer: (A)

$\frac{1}{a}$

Put $x=x+a$

$\underset{x\to 0}{lim}\frac{\log (x+a)-\log a}{\tan x}$

$=\underset{x\to 0}{lim}\frac{\log \left(\frac{a+x}{a}\right)}{\frac{\tan x}{x}\frac{x}{a}}a$ (use formula)

$=\frac{1}{a}$