A calculus problem by Yeldo Pailo

Calculus Level 2

$lim _{ x\rightarrow 0 }{ \quad } \frac { \log { (1+ax)- } \log { (1-bx) } }{ x }$

ab does not exist a-b a+b none of these 0 1 a/b

1 solution

Anandhu Raj
Apr 12, 2015

We have $lim _{ x\rightarrow 0 }{ \quad } \frac { \log { (1-ax)- } \log { (1-bx) } }{ x }$

By using LHR,

$\lim _{ x\to 0 } \frac { f'(\log { (1+ax)- } \log { (1-bx)) } }{ f'(x) }$

On solving,

$\lim _{ x\rightarrow 0 }{ \frac { a }{ 1-ax } } -\frac { -b }{ 1-bx } =\boxed { a+b }$

I think the correct answer is 'b-a'. The derivative of log(1-ax) should be (-a)/(1-ax). Unless I am missing something...

Krishnan Shankar - 6 years, 2 months ago

@Krishnan Shankar Oops..You are right.Even I didn't notice that while writing solution..:(

Anandhu Raj - 6 years, 2 months ago

@Krishnan Shankar Now I have corrected it !!

Yeldo Pailo - 6 years, 2 months ago