limx tends to a ((x+2)^5/3-(a+2)^5/3)/x-2

Dear Student,

I think there should be (x-a) in the denominator.

Please find below the solution to the asked query :

$$\begin{gathered} \underset{\mathrm{x}\to \mathrm{a}}{\lim }\frac{{\left(\mathrm{x}+2\right)}^{5/3} - {\left(\mathrm{a}+2\right)}^{5/3}}{\mathrm{x} - \mathrm{a}} \\ =\underset{\mathrm{x}\to \mathrm{a}}{\lim }\frac{{\left(\mathrm{x}+2\right)}^{5/3} - {\left(\mathrm{a}+2\right)}^{5/3}}{\left(\mathrm{x}+2\right)-\left(\mathrm{a}+2\right)} \\ =\frac{5}{3}{\left(\mathrm{a}+2\right)}^{5/3-1} \left[\mathrm{as}, \underset{\mathrm{x}\to \mathrm{a}}{\lim }\frac{{\mathrm{x}}^{\mathrm{n}} - {\mathrm{a}}^{\mathrm{n}}}{\mathrm{x} - \mathrm{a}} = {\mathrm{na}}^{\mathrm{n}-1}\right] \\ =\frac{5}{3}{\left(\mathrm{a}+2\right)}^{2/3} \end{gathered}$$

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