Question

lim(x->-1) 4x²+3x-1/x²+2x+1 ​

Answer 1

Ответ:

$\frac{lim}{x - > 1}( \frac{ {4x}^{2} + 3x - 1}{ {x}^{2} + 2x + 1 } )$

$\frac{ \frac{lim}{x - > 1}( {4x}^{2} + 3x - 1)}{ \frac{lim}{x - > 1} ( {x}^{2} + 2x + 1)}$

$\frac{ \frac{lim}{x - > 1}( {4x}^{2} + 3x) - \frac{lim}{x - > 1} (1) }{ \frac{lim}{x - > 1} ( {x}^{2} + 2x) + \frac{lim}{x - > 1}(1) }$

$\frac{ \frac{lim}{x - > 1}( {4x}^{2}) + \frac{lim}{x - > 1}(3x) - 1 }{ \frac{lim}{x - > 1} ( {x}^{2} ) + \frac{lim}{x - > 1}(2x) + 1 }$

$\frac{4 \times \frac{lim}{x - > 1} ( {x}^{2}) + 3 \times \frac{lim}{x - > 1} (x) - 1 }{ {( \frac{lim}{x - > 1} (x))}^{2} + 2 \times \frac{lim}{x - > 1} (x) + 1 }$

$\frac{4 \times {( \frac{lim}{x - > 1} (x))}^{2} + 3 \times 1 - 1 }{ {1}^{2} + 2 \times 1 + 1}$

$\frac{4 \times {1}^{2} + 3 \times 1 - 1 }{ {1}^{2} + 2 \times 1 + 1}$

$\frac{4 \times 1 + 3 - 1}{1 + 2 + 1}$

$\frac{4 + 3 - 1}{1 + 2 + 1}$

$\frac{6}{4}$

сокращаем на общий делитель 2:

$\frac{3}{2}$