Find the limit of ((t+4)^(1/2)(t-2)^4)/((3t-6)^2) as t approaches 2

 Exercise

$\lim_{x\to2}\frac{\sqrt{\left(t+4\right)}\left(t-2\right)^4}{\left(3t-6\right)^2}$

 

Factor the polynomial $\left(3t-6\right)$ by it's greatest common factor (GCF): $3$

$\lim_{t\to2}\left(\frac{\sqrt{t+4}\left(t-2\right)^4}{\left(3\left(t-2\right)\right)^2}\right)$

 

The power of a product is equal to the product of it's factors raised to the same power

$\lim_{t\to2}\left(\frac{\sqrt{t+4}\left(t-2\right)^4}{9\left(t-2\right)^2}\right)$

 

Simplify the fraction $\frac{\sqrt{t+4}\left(t-2\right)^4}{9\left(t-2\right)^2}$ by $t-2$

$\lim_{t\to2}\left(\frac{\sqrt{t+4}\left(t-2\right)^{2}}{9}\right)$

 

Evaluate the limit $\lim_{t\to2}\left(\frac{\sqrt{t+4}\left(t-2\right)^{2}}{9}\right)$ by replacing all occurrences of $t$ by $2$

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