Question

find the limit of (x root x-m root m)/1-x^-2/3 when x tends to infinity.

Answer 1

Dear student

$$\begin{gathered} \underset{\mathrm{x}\to \infty }{\lim }\frac{\mathrm{x}\sqrt{\mathrm{x}}-\mathrm{m}\sqrt{\mathrm{m}}}{1-{\mathrm{x}}^{{\displaystyle \raisebox{1ex}{$-2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}} \\ =\frac{\underset{\mathrm{x}\to \infty }{\lim }\left[\mathrm{x}\sqrt{\mathrm{x}}-\mathrm{m}\sqrt{\mathrm{m}}\right]}{\underset{\mathrm{x}\to \infty }{\lim }\left(1-{\mathrm{x}}^{{\displaystyle \frac{-2}{3}}}\right)} \\ =\frac{\infty }{1-{\infty }^{{\displaystyle \frac{-2}{3}}}} \\ =\frac{\infty }{1-0} \\ =\infty \end{gathered}$$
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