What is the limit as x approaches 0+of (x^2)/8-6/x ?

The limit as x approaches 0+of (x^2)/8-6/x is -infinity

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limit as x approaches 0+of (x^2)/8-6/x

x \to 0 + lim (\frac{x ^{2}}{8} - \frac{6}{x})

- \infty

Solution steps

x \to 0 + lim (\frac{x ^{2}}{8} - \frac{6}{x})

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

With the exception of indeterminate form

= x \to 0 + lim (\frac{x ^{2}}{8}) - x \to 0 + lim (\frac{6}{x})

x \to 0 + lim (\frac{x ^{2}}{8}) = 0

x \to 0 + lim (\frac{6}{x}) = \infty

= 0 - \infty

Apply Infinity Property:

c - \infty = - \infty

= - \infty

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\frac{d y}{d x} = - 10 y, y (0) = 5

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What is the limit as x approaches 0+of (x^2)/8-6/x ?
The limit as x approaches 0+of (x^2)/8-6/x is -infinity