Answer
$=\tan 4 \approx 1.158$
Work Step by Step
$\lim _{t\rightarrow 4} \tan\dfrac {t-4}{\sqrt {t}-2}=\tan\dfrac {\left( \sqrt {t}\right) ^{2}-22}{\sqrt {t}-2}=\tan\dfrac {\left( \sqrt {t}-2\right) \left( \sqrt {t}+2\right) }{\left( \sqrt {t}-2\right) }=\tan(\sqrt {t}+2)=\tan\sqrt ( {4}+2)=\tan 4 \approx 1.158$
