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

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

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

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

- 1

Solution steps

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

x \to 0 + lim (1) = 1

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

= - 1 + 0

Simplify

= - 1

h (x) \to 0 lim ((x + h (x))^{n})

x \to 2 lim (\frac{x ^{2} + 5 x - 14}{x ^{2} - 11 x + 18})

x \to - 1 lim (4 x + 3)

x \to - 1 lim (\frac{7 x + 3}{x + 1})

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

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