What is the limit as x approaches 0+of-1+ln(x)(x) ?

The limit as x approaches 0+of-1+ln(x)(x) is -1

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limit as x approaches 0+of-1+ln(x)(x)

x \to 0 + lim (- 1 + ln (x) (x))

- 1

Solution steps

x \to 0 + lim (- 1 + ln (x) 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 (1) + x \to 0 + lim (ln (x) x)

x \to 0 + lim (1) = 1

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

= - 1 + 0

Simplify

= - 1

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

x \to - 5 lim (\frac{x + 5}{x})

x \to 3 lim (\frac{0}{0})

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

x \to - 2 lim (x^{2} + 2 x + 5)

What is the limit as x approaches 0+of-1+ln(x)(x) ?
The limit as x approaches 0+of-1+ln(x)(x) is -1