What is the limit as t approaches 2 of (t+2)^{3/2}(2t+4)^{1/3} ?

The limit as t approaches 2 of (t+2)^{3/2}(2t+4)^{1/3} is 16

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limit as t approaches 2 of (t+2)^{3/2}(2t+4)^{1/3}

t \to 2 lim ((t + 2)^{\frac{3}{2}} (2 t + 4)^{\frac{1}{3}})

16

Solution steps

t \to 2 lim ((t + 2)^{\frac{3}{2}} (2 t + 4)^{\frac{1}{3}})

Plug in the value

t = 2

= (2 + 2)^{\frac{3}{2}} (2 \cdot 2 + 4)^{\frac{1}{3}}

Simplify

(2 + 2)^{\frac{3}{2}} (2 \cdot 2 + 4)^{\frac{1}{3}} : 16

= 16

\int_{\frac{1}{7}}^{3} 16 x ln (7 x) d x

\int_{0}^{4} 17 d x

\int_{1}^{t} \frac{37}{x ^{3}} d x

y^{^{'}} = - x^{2} - \frac{1}{x} \cdot y

\int \frac{1}{1 - 64 x ^{2}} d x

What is the limit as t approaches 2 of (t+2)^{3/2}(2t+4)^{1/3} ?
The limit as t approaches 2 of (t+2)^{3/2}(2t+4)^{1/3} is 16