What is the limit as x approaches-1+of (x-3)/(x^2+x) ?

The limit as x approaches-1+of (x-3)/(x^2+x) is infinity

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limit as x approaches-1+of (x-3)/(x^2+x)

x \to - 1 + lim (\frac{x - 3}{x ^{2} + x})

\infty

Solution steps

x \to - 1 + lim (\frac{x - 3}{x ^{2} + x})

\frac{x - 3}{x ^{2} + x} = (x - 3) \frac{1}{x ^{2} + x}

= x \to - 1 + lim ((x - 3) \frac{1}{x ^{2} + x})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to - 1 + lim (x - 3) \cdot x \to - 1 + lim (\frac{1}{x ^{2} + x})

x \to - 1 + lim (x - 3) = - 4

x \to - 1 + lim (\frac{1}{x ^{2} + x}) = - \infty

= (- 4) (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

x \to - 2 lim (2 x^{3} - x^{2} + 4 x + 1)

x \to \infty lim (x - \frac{1}{2})

x \to - 1 lim (x^{2} - 2 x + 1)

x \to 3 + lim (\frac{x}{x ^{2} - 9})

x \to 0 lim ((5 x)^{s i n (x)})

What is the limit as x approaches-1+of (x-3)/(x^2+x) ?
The limit as x approaches-1+of (x-3)/(x^2+x) is infinity