Question

Решите пожалуйста лимит, даю максимум баллов.

Answer 1

${e}^{lim(x - > a)((u(x) - 1) \times v(x))} \\ u(x) = \frac{2x + 3}{5 + x} \\ v(x) = \frac{1}{ {x}^{2} - x - 2} \\ lim(x - > 2) ((\frac{2x + 3}{5 + x} - 1) \times \frac{1}{ {x}^{2} - x - 2}) = lim(x - > 2)( \frac{2x + 3 - 5 - x}{5 + x} ) \times \frac{1}{{x}^{2} - x - 2} = lim(x - > 2)(\frac{x - 2}{5 + x} \times \frac{1}{(x - 2)(x + 1}) = lim(x - > 2)( \frac{1}{(5 + x)(x + 1)} = \frac{1}{21} = > {e}^{ \frac{1}{21} }$

Answer 2

$( \frac{2x + 3}{5 + x} )^{\frac{1}{x^2 - x - 2} } = ( \frac{x + 5 + x - 2}{x + 5} )^{\frac{1}{(x-2)(x+1)} } = (1 + \frac{x - 2}{x + 5} )^{\frac{x+5}{x-2} * \frac{1}{(x+1)(x+5)} } -> \{ \frac{x-2}{x+5} -> 0 \} -> e^{ \frac{1}{(x+1)(x+5)} } -> e^{1/21}$