d: \(\lim_{x\to3}\frac{2-\sqrt[3]{x+5}}{x^2-9}\)
\(=\lim_{x\to3}\frac{8-x-5}{\left(4+2\sqrt[3]{x+5}+\sqrt[3]{\left(x+5\right)^2}\right)\cdot\left(x-3\right)\left(x+3\right)}\)
\(=\lim_{x\to3}\frac{3-x}{\left(4+2\sqrt[3]{x+5}+\sqrt[3]{\left(x+5\right)^2}\right)\cdot\left(x-3\right)\left(x+3\right)}\)
\(=\lim_{x\to3}\frac{-1}{\left(4+2\sqrt[3]{x+5}+\sqrt[3]{\left(x+5\right)^2}\right)\cdot\left(x+3\right)}\)
\(=-\frac{1}{\left(4+2\cdot\sqrt[3]{3+5}+\sqrt[3]{\left(3+5\right)^2}\right)\left(3+3\right)}=\frac{-1}{\left(4+2\cdot2+4\right)\cdot6}=-\frac{1}{6\cdot12}=-\frac{1}{72}\)
e: \(\lim_{x\to1}\frac{\sqrt[3]{2x-1}-1}{\sqrt{3x+1}-2}\)
\(=\lim_{x\to1}\frac{2x-1-1}{\left(\sqrt[3]{\left(2x-1\right)^2}+\sqrt[3]{2x-1}+1\right)}:\frac{3x+1-4}{\sqrt{3x+1}+2}\)
\(=\lim_{x\to1}\frac{2x-2}{\left(\sqrt[3]{\left(2x-1\right)^2}+\sqrt[3]{2x-1}+1\right)}:\frac{3x-3}{\sqrt{3x+1}+2}\)
\(=\lim_{x\to1}\frac{2\left(x-1\right)}{\left(\sqrt[3]{\left(2x-1\right)^2}+\sqrt[3]{2x-1}+1\right)}\cdot\frac{\sqrt{3x+1}+2}{3\left(x-1\right)}\)
\(=\lim_{x\to1}\frac{2}{\left(\sqrt[3]{\left(2x-1\right)^2}+\sqrt[3]{2x-1}+1\right)}\cdot\frac{\sqrt{3x+1}+2}{3}\)
\(=\frac{2}{\left(\sqrt[3]{\left(2\cdot1-1\right)^2}+\sqrt[3]{2\cdot1-1}+1\right)}\cdot\frac{\sqrt{3\cdot1+1}+2}{3}=\frac{2}{\left(\sqrt[3]{1}+\sqrt[3]{1}+1\right)}\cdot\frac{2+2}{3}=\frac23\cdot\frac43=\frac89\)
