Question

by indetrminate forms

Answer 1

$\lim_{x \to a} \frac{x \sqrt{x} - a \sqrt{a} }{x - a} \\ = \lim_{x \to a} \frac{(x \sqrt{x} - a \sqrt{a} )( x \sqrt{x} + a \sqrt{a} )}{(x - a)(x \sqrt{x} + a \sqrt{a} )} \\ = \lim_{x \to a} \frac{( {x}^{3} - {a}^{3} )}{(x - a)(x \sqrt{x} + a \sqrt{a} )} \\ = \lim_{x \to a} \frac{(x - a )( {x}^{2} + xa + {a}^{2} )}{(x - a)(x \sqrt{x} + a \sqrt{a} )} \\ = \lim_{x \to a} \frac{( {x}^{2} + xa + {a}^{2} )}{(x \sqrt{x} + a \sqrt{a} )} \\ = \frac{( {a}^{2} + a \times a + {a}^{2} )}{(a\sqrt{a} + a \sqrt{a} )} \\ = \frac{3 {a}^{2} }{2a \sqrt{a} } = \frac{3 \sqrt{a} }{2}$

Answer 2

I hope you got your answer