Evaluate

Question:

Evaluate

$\lim _{x \rightarrow a}\left(\frac{x^{5 / 2}-a^{5 / 2}}{x-a}\right)$

 

Solution:

To evaluate:

$\lim _{x \rightarrow a} \frac{x^{\frac{5}{2}}-a^{\frac{5}{2}}}{x-a}$

Formula used: We have,

$\frac{x^{m}-y^{m}}{x-y}=m y^{m-1}$

As $x \rightarrow$ a, we have

$\lim _{x \rightarrow a} \frac{x^{\frac{5}{2}}-a^{\frac{5}{2}}}{x-a}=\frac{5}{2} a^{\frac{5}{2}-1}$

$\lim _{x \rightarrow a} \frac{x^{\frac{5}{2}}-a^{\frac{5}{2}}}{x-a}=\frac{5}{2} a^{\frac{3}{2}}$

Thus, the value of $\lim _{x \rightarrow a} \frac{x^{\frac{5}{2}}-a^{\frac{5}{2}}}{x-a}$ is $\frac{5}{2} a^{\frac{3}{2}}$

 

 

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