Question

помогите решить пределы пожалуйста!

Answer 1

3)
$lim frac{ sqrt{1 - x} - 3 }{2 + sqrt[3]{x} } = ( frac{0}{0} ) = limfrac{ frac{ -1}{2 sqrt{1 - x} } }{ frac{1}{3} times {x}^{ - frac{2}{3 } } } = lim frac{ - 3 {x}^{ frac{2}{3} } }{2 sqrt{1 - x} } = frac{ - 3 times sqrt[3]{64} }{2 sqrt{9} } = frac{ - 3 times 4}{2 times 3} = - 2$
4)
$lim frac{ {x}^{3} + 1}{2 + 3x + 5 {x}^{3} } = lim frac{3 {x}^{2} }{3 + 15 {x}^{2} } = lim frac{6x}{30x} = frac{6}{30} = frac{1}{5}$

Answer 2

$1); ; limlimits _{x to -8}frac{sqrt{1-x}-3}{2+sqrt[3]{x}}=limlimits _{x to -8}frac{(1-x-9)(4-2sqrt[3]{x}+sqrt[3]{x^2})}{(sqrt{1-x}+3)(8+x)}=\\=limlimits _{x to -8}frac{-(8+x)(4-2sqrt[3]{x}+sqrt[3]{x^2})}{(sqrt{1-x}+3)(8+x)}=frac{-(4+4+4)}{3+3}=-frac{12}{9}=-frac{4}{3}\\2); ; limlimits _{x to infty }frac{x^3+1}{2+3x+5x^3}=limlimits _{x to infty}frac{x^3}{5x^3} =frac{1}{5}$