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

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

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

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

\infty

Solution steps

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

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

x \to 0 + lim (2 x) = 0

x \to 0 + lim (ln (\frac{x}{3})) = - \infty

= - 0 - (- \infty)

Simplify

- 0 - (- \infty) : \infty

= \infty

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

x \to 2 lim (5 - x)

r \to 0 lim (1 + \frac{1}{r} + \frac{1}{r ^{2}})

x \to 0 lim (\frac{1 0 ^{x} - 5 ^{x}}{x})

x \to - \infty lim (5 x - 1)

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