Question

qual o resultado ?!!

Answer 1

x² + x - 6 = (x-2)(x+3)

1/(x-2) + (x-7)/(x-2)(x+3)

[(x+3) + (x-7)]/(x-2)(x+3)

(2x-4)/(x-2)(x+3)

2(x-2)/(x-2)(x+3)

2/(x+3)

lim x->2 2/(x+3) = 2/(2+3) = 2/5

Resposta: 2/5

Answer 2

Resposta:

$\boxed{0,4}$

Explicação passo-a-passo:

$\lim_{x \to 2} ( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + x - 6 } )$

$\lim_{x\to {2}^{ - } }( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + x - 6 } ) \\ \lim_{x \to {2}^{ + } }( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + x - 6 } )$

1° vou resolver a de cima:

$\lim_{x \to {2}^{ - } } ( \frac{1}{x - 2} ) \\ \lim_{x \to {2}^{ - } } ( \frac{x - 7}{ {x}^{2} + x - 6} )$

$- \infty \\ + \infty$

$\lim_{x \to {2}^{ - } } ( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + x - 6} )$

$\lim_{x \to {2}^{ - } } ( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + 3x - 2x - 6} )$

$\lim_{x \to {2}^{ - } } ( \frac{1}{x - 2} + \frac{x - 7}{ x \times (x + 3) - 2x - 6} )$

$\lim_{x \to {2}^{ - } } ( \frac{1}{x - 2} + \frac{x - 7}{x \times (x + 3) - 2(x + 3)} )$

$\lim_{x \to {2}^{ - } } ( \frac{1}{x - 2} + \frac{x - 7}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ - } } ( \frac{x + 3 + x - 7}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ - } } ( \frac{2x + 3 - 7}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ - } } ( \frac{2x - 4}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ - } } ( \frac{2(x - 2)}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ - } } ( \frac{2}{x + 3} )$

$\frac{2}{2 + 3}$

$\boxed{ \frac{2}{5} }$

Agora vamos fazer a 2°:

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + x - 6 } )$

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} ) \\ \lim_{x \to {2}^{ + } } ( \frac{x - 7}{ {x}^{2} + x - 6 } )$

$+ \infty \\ - \infty$

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} + \frac{x -7 }{ {x}^{2} + x - 6 } )$

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} + \frac{x - 7}{ {x}^{2} + 3x - 2x - 6} )$

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} + \frac{x - 7}{x \times (x + 3) - 2x - 6} )$

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} + \frac{x - 7}{x \times (x + 3) - 2(x + 3)} )$

$\lim_{x \to {2}^{ + } } ( \frac{1}{x - 2} + \frac{x - 7}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ + } } ( \frac{x + 3 + x - 7}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ + } } ( \frac{2x + 3 - 7}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ + } } ( \frac{2x - 4}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ + } } ( \frac{2(x - 2)}{(x + 3) \times (x - 2)} )$

$\lim_{x \to {2}^{ + } } ( \frac{2}{x + 3} )$

$\frac{2}{2 + 3}$

$\boxed{ \frac{2}{5} }$

Agora vamos juntá-las:

$\frac{ \frac{ \frac{2}{5} }{2} }{5}$

Como os limites são inguais, consequentemente vai ficar assim:

$\frac{2}{5}$

$\boxed{0,4}$

ATT:ARMANDO