Question

lim x → 0 tan^-1 ( ax ) /tan^-1 ( b x ) evaluate without using lahospital rule.

Answer 1

Step-by-step explanation:

We have,

$\lim _{x \rarr0 } \frac{ \tan^{ - 1} (ax) }{ \tan^{ - 1} (bx) }$

$= \lim _{x \rarr0 } \frac{ \tan^{ - 1} (ax) \times bx}{ax \times \tan^{ - 1} (bx) } \times \frac{a}{b}$

$= \frac{a}{b} \times \frac{\lim _{x \rarr0} \frac{ \tan^{ - 1} (ax) }{ax} }{ \lim _{x \rarr0} \frac{ \tan^{ - 1} (bx) }{bx} }$

$= \frac{a}{b}$