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

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

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limit as x approaches 0+of x-ln(x)

x \to 0 + lim (x - ln (x))

\infty

Solution steps

x \to 0 + lim (x - ln (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 (x) - x \to 0 + lim (ln (x))

x \to 0 + lim (x) = 0

x \to 0 + lim (ln (x)) = - \infty

= 0 - (- \infty)

Simplify

0 - (- \infty) : \infty

= \infty

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2 t (\frac{d y}{d t}) + y = 4 t^{2} + 3 t

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\int \frac{1}{e ^{x}} d x

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