Question

can anyone answer this question​

Answer 1

$\displaystyle \lim_{x \to \: 0} ( \frac{ {3}^{x} - 1 }{ \sqrt{1 + x} - 1} )$

Evaluate using L'Hopital's Rule.

$\displaystyle \: \lim_{x \to \: 0}( \frac{ \frac{d}{dx} ( {3}^{x} - 1)}{ \frac{d}{dx}( \sqrt{1 + x} - 1) } )$

Calculate the derivatives.

$\displaystyle \lim_{x \to 0}( \frac{ ln(3) \times {3}^{x} }{ \dfrac{1}{2 \sqrt{1 + x} } } )$

Simplify.

$\displaystyle \lim_{x \to 0}(2 ln(3) \times {3}^{x} \times \sqrt{1 + x} )$

$\displaystyle 2 ln(3) \times {3}^{0} \times \sqrt{1 + 0}$

$\boxed{\green{{ \green{2 ln(3) }}}}$

Answer 2

answer:

2ln (3)

the way is stated up