Question

the value of Lim x-0 , log (5-x) - log (5+x)/x is...

Answer 1

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{\lim_{x\to\;0}\;\dfrac{log(5-x)-log(5+x)}{x}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\lim_{x\to\;0}\;\dfrac{log(5-x)-log(5+x)}{x}}$

$\textsf{when applying limits}$

$=\mathsf{\dfrac{0}{0}\;form}$

$\textsf{By applying L Hopital's rule}$

$=\mathsf{\lim_{x\to\;0}\;\dfrac{\dfrac{-1}{5-x}-\dfrac{1}{5+x}}{1}}$

$=\mathsf{-\dfrac{1}{5}-\dfrac{1}{5}}$

$=\mathsf{\dfrac{-2}{5}}$

$\implies\boxed{\mathsf{\lim_{x\to\;0}\;\dfrac{log(5-x)-log(5+x)}{x}=\dfrac{-2}{5}}}$

$\textbf{Find more:}$

Lim. 8x³-1 / 16x4-1

x--->1/2

https://brainly.in/question/6423235

Lt x=0 (cos7X-cos9X)/(cosX-cos5X)

https://brainly.in/question/6057974

If f(2)=4 and f'(2)=1, then find lim x tends to 2 xf(2)-2f(x)/x-2

https://brainly.in/question/5808208