Question

Нужно решить 29 задание

Answer 1

$1); ; limlimits _{x to -2} frac{3x^2+5x-8}{2x^2+3x-5}= frac{3cdot 4-5cdot 2-8}{2cdot 4-3cdot 2-5} = frac{-6}{-3} =2\\ limlimits _{x to 1} frac{3x^2+5x-8}{2x^2+3x-5}= limlimits _{x to 1}frac{3(x-1)(x+frac{8}{3})}{2(x-1)(x+frac{5}{2})} = limlimits _{x to 1} frac{3+8x}{2x+5} = frac{11}{7}\\ limlimits _{x to infty } frac{3x^2+5x-8}{2x^2+3x-5}= limlimits _{x to infty} frac{3+frac{5}{x}-frac{8}{x^2}}{2+frac{3}{x}-frac{5}{x^2}} = frac{3}{2}$

$2); ; limlimits _{x to 3} frac{ sqrt{x-2}-sqrt{4-x} }{x-3}= limlimits _{x to 3} frac{(x-2)-(4-x)}{(x-3)( sqrt{x-2}+sqrt{4-x})}=\\= limlimits _{x to 3} frac{2(x-3)}{(x-3)( sqrt{x-2}+sqrt{4-x} )}= limlimits _{x to 3}frac{2}{ sqrt{x-2}+sqrt{4-x} }= frac{2}{ sqrt{1}+sqrt{1}}=1$

$3); ; limlimits _{x to 0} frac{sin3x}{tg2x}= limlimits _{x to 0}frac{3x}{2x}= frac{3}{2}\\4); ; limlimits _{n to infty}Big (frac{5n-3}{5n+4}Big )^{n+4}= limlimits _{n to infty}Big (underbrace {Big (1+frac{-7}{5n+4}Big )^{ frac{5n+4}{-7}}}_{e}Big )^{ frac{-7(n+4)}{5n+4} }=\\=e^{ limlimits _{n to infty} frac{-7n-28}{5n+4} }=e^{-frac{7}{5}}$

Answer 2

Благодарствую