Question

Evaluate:lim x 0 a^ x +b^ x -2/ x​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\displaystyle\rm{\lim_{x\to0}\dfrac{{a}^{x}+{b}^{x}-2}{x}}$

$\displaystyle\rm{=\lim_{x\to0}\dfrac{{a}^{x}-1+{b}^{x}-1}{x}}$

$\displaystyle\rm{=\lim_{x\to0}\dfrac{{a}^{x}-1}{x}+\lim_{x\to0}\dfrac{{b}^{x}-1}{x}}$

$\displaystyle\rm{=\ln(a)+\ln(b)}$

$\displaystyle\rm{=\ln\left(\dfrac{a}{b}\right)}$

Answer 2

2

Your answer is - ______

x