MCQ
$\lim_{y \rightarrow 0} \frac{\sqrt[3]{y}+\sqrt[3]{{{y}^{2}}}-\sqrt[4]{{{y}^{3}}}}{\sqrt[3]{y}+\sqrt{y}+\sqrt[4]{{{y}^{3}}}}$
- A$-1$
- Bલક્ષનું અસ્તિત્વ નથી.
- ✓$1$
- D$0$
$\lim_{y \rightarrow 0}\frac{\sqrt[3]{y}+\sqrt[3]{y^2}-\sqrt[4]{y^3}}{\sqrt[3]{y}+\sqrt{y}+\sqrt[4]{y^3}}$
$=\lim_{y \rightarrow 0} \frac{{y^\frac{1}{3}+y^{\frac{2}{3}}-y^{\frac{3}{4}}}}{{y^\frac{1}{3}+y^{\frac{1}{2}}+y^{\frac{3}{4}}}}$
$\left(\frac{0}{0}\right)from$
$=\lim_{y \rightarrow 0} \frac{y^{\frac{1}{3}}\left(1+y^{\frac{2}{3}-\frac{1}{3}}-y^{\frac{3}{4}-\frac{1}{3}}\right)}{y^\frac{1}{3}\left(1+y^{\frac{1}{2}-\frac{1}{3}}+y^{\frac{3}{4}-\frac{1}{3}}\right)}$
$=\lim_{y \rightarrow 0} \frac{1+y^{\frac{1}{3}}-y^{\frac{5}{12}}}{1+y^{\frac{1}{6}}+y^{\frac{5}{12}}}$
$=1$
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