Question

Evaluate:
$\rm \displaystyle \lim_{x \to 0}\ \frac{3^{x}-5^{x}}{x}$

Answer 1

❤see in the given pic their is an answer

Answer 2

Answer:

$log\frac{3}{5}$

Step-by-step explanation:

SInce we need to evaluate the $\rm \displaystyle \lim_{x \to 0}\ \frac{3^{x}-5^{x}}{x}$

Apply directly $\lim_{x\to 0}$ we get ,

$\frac{3^{0}-5^{0}}{0}$= $\frac{1-1}{0}$= $\frac{0}{0}$  (we know that $3^{0} =1\ and\ 5^{0} = 1$ )

So, apply L'Hospital rule (Differentiate the function with respect to its variable x ) we get,

We get ,$\frac{3^{x}log3-5^{x}log5 }{1}$.

So, apply limit

$\frac{3^{0}log3-5^{0}log5 }{1} = log\frac{3}{5}$

So, $\rm \displaystyle \lim_{x \to 0}\ \frac{3^{x}-5^{x}}{x}$ = $log\frac{3}{5}$