What is the limit as y approaches 0 of 2/(y^2+y)-2/y ?

The limit as y approaches 0 of 2/(y^2+y)-2/y is -2

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limit as y approaches 0 of 2/(y^2+y)-2/y

y \to 0 lim (\frac{2}{y ^{2} + y} - \frac{2}{y})

- 2

Solution steps

y \to 0 lim (\frac{2}{y ^{2} + y} - \frac{2}{y})

Multiply by the conjugate of

\frac{2}{y ^{2} + y} - \frac{2}{y} : \frac{\frac{4}{y ^{4} + 2 y ^{3} + y ^{2}} - \frac{4}{y ^{2}}}{\frac{2}{y ^{2} + y} + \frac{2}{y}}

= y \to 0 lim (\frac{\frac{4}{y ^{4} + 2 y ^{3} + y ^{2}} - \frac{4}{y ^{2}}}{\frac{2}{y ^{2} + y} + \frac{2}{y}})

Simplify

\frac{\frac{4}{y ^{4} + 2 y ^{3} + y ^{2}} - \frac{4}{y ^{2}}}{\frac{2}{y ^{2} + y} + \frac{2}{y}} : - \frac{2}{y + 1}

= y \to 0 lim (- \frac{2}{y + 1})

Plug in the value

y = 0

= - \frac{2}{0 + 1}

Simplify

= - 2

f (x) = 2^{l n (x)}

6 x^{2} - 9 x - 6, 7 x^{2} - 5 x - 3

x \to 0 lim (\frac{x}{5})

(x^{2} - 9)^{2} + 2

7 x (x + 3 y) y^{^{'}} = 7 y (x - 3 y)

What is the limit as y approaches 0 of 2/(y^2+y)-2/y ?
The limit as y approaches 0 of 2/(y^2+y)-2/y is -2