Question

$\lim_{t \to 4} \frac{\sqrt{t} -2}{t-4}$

Answer 1

Explicação passo-a-passo:

$\sf \lim_{t\to~4}~\dfrac{\sqrt{t}-2}{t-4}$

$\sf =\lim_{t\to~4}~\dfrac{\sqrt{t}-2}{t-4}\cdot\dfrac{\sqrt{t}+2}{\sqrt{t}+2}$

$\sf =\lim_{t\to~4}~\dfrac{(\sqrt{t})^2-2^2}{(t-4)\cdot(\sqrt{t}+2)}$

$\sf =\lim_{t\to~4}~\dfrac{(t-4)}{(t-4)\cdot(\sqrt{t}+2)}$

$\sf =\lim_{t\to~4}~\dfrac{1}{\sqrt{t}+2}$

$\sf =\dfrac{1}{\sqrt{4}+2}$

$\sf =\dfrac{1}{2+2}$

$\sf =\dfrac{1}{4}$