Calculus Function problem

[newton333]

 

anyone can explain me why

[Prometheus]

Try factorising the numerator.

[Crimson Sunbird]

What do you mean by [latex]\frac{-2}{0}=-\infty[/latex]?

[mathematic]

The numerator is negative for x ~ -1. The denominator switches sign at x = -1. For x > -1 (~1), the denomiator is negative. As a result the ratio is positive.

 

Another way, using your analysis is (-1 + ε)^2 - 1 ~ 1 -2ε -1 = -2ε. This gives a + sign to your ratio.

[newton333]

thank you