If we directly evaluate the limit $\lim_{t\to 4}\left(\frac{t-4}{3\left(\sqrt{t}-2\right)}\right)$ as $t$ tends to $4$, we can see that it gives us an indeterminate form
$\frac{0}{0}$
2
We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately
Evaluate the limit $\lim_{t\to4}\left(\frac{1}{\frac{3}{2}t^{-\frac{1}{2}}}\right)$ by replacing all occurrences of $t$ by $4$
$\frac{1}{\frac{3}{2}\cdot 4^{-\frac{1}{2}}}$
5
Calculate the power $4^{-\frac{1}{2}}$
$\frac{1}{\frac{3}{2}\frac{1}{2}}$
6
Multiply $\frac{3}{2}$ times $\frac{1}{2}$
$\frac{1}{\frac{3}{4}}$
7
Divide $1$ by $\frac{3}{4}$
$\frac{4}{3}$
Final answer to the problem
$\frac{4}{3}$
Exact Numeric Answer
$1.3333$
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