What is the limit as x approaches 0+of 7/x-3/(x^2) ?

The limit as x approaches 0+of 7/x-3/(x^2) is -infinity

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limit as x approaches 0+of 7/x-3/(x^2)

x \to 0 + lim (\frac{7}{x} - \frac{3}{x ^{2}})

- \infty

Solution steps

x \to 0 + lim (\frac{7}{x} - \frac{3}{x ^{2}})

Multiply by the conjugate of

\frac{7}{x} - \frac{3}{x ^{2}} : \frac{\frac{49}{x ^{2}} - \frac{9}{x ^{4}}}{\frac{7}{x} + \frac{3}{x ^{2}}}

= x \to 0 + lim (\frac{\frac{49}{x ^{2}} - \frac{9}{x ^{4}}}{\frac{7}{x} + \frac{3}{x ^{2}}})

Simplify

\frac{\frac{49}{x ^{2}} - \frac{9}{x ^{4}}}{\frac{7}{x} + \frac{3}{x ^{2}}} : \frac{7 x - 3}{x ^{2}}

= x \to 0 + lim (\frac{7 x - 3}{x ^{2}})

\frac{7 x - 3}{x ^{2}} = (7 x - 3) \frac{1}{x ^{2}}

= x \to 0 + lim ((7 x - 3) \frac{1}{x ^{2}})

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 0 + lim (7 x - 3) \cdot x \to 0 + lim (\frac{1}{x ^{2}})

x \to 0 + lim (7 x - 3) = - 3

x \to 0 + lim (\frac{1}{x ^{2}}) = \infty

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches 0+of 7/x-3/(x^2) ?
The limit as x approaches 0+of 7/x-3/(x^2) is -infinity