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

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

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

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

0

Solution steps

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

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

x \to 0 + lim (x) = 0

= 0 - 0

Simplify

= 0

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x \to 4 + lim (\frac{1}{4 - x})

x \to 1 lim (lo g_{2} (8 x))

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

x \to 0 lim ((x + sin (x))^{x})

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