Question

Write the value of ${lim}_{x\to 0^{-}}\frac{\sin x}{\sqrt{x}}$

Answer 1

${lim}_{x\to 0^{-}}\frac{\sin x}{\sqrt{x}}={lim}_{h\to 0}\frac{\sin (0-h)}{(0-h{)}^{\frac{1}{2}}}={lim}_{h\to 0}\frac{-\sin h}{(-h{)}^{\frac{1}{2}}}={lim}_{h\to 0}\frac{-\sin h}{-h}(-h{)}^{\frac{1}{2}}=li{m}_{h\to 0}(-h{)}^{\frac{1}{2}}$