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

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

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

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

- \infty

Solution steps

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 + lim (x + 1) \cdot x \to 0 + lim (ln (x))

x \to 0 + lim (x + 1) = 1

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

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to 3 lim ((5 x^{2})^{0})

x \to 4 lim (a x^{2} + b x + 4)

x \to 0 lim (x x)

x \to \infty lim ((ln (x))^{\frac{3}{x}})

x \to a lim ([f (x) + g (x)])

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