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

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

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

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

0

Solution steps

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

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

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

Rewrite for L'Hopital

= - x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

= - x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Simplify

\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}} : - x

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

Plug in the value

x = 0

= - (- 0)

Simplify

= 0

\int \frac{x - 2}{x ^{2} - 4 x + 3} d x

f (x) = ln (e^{x} + x e^{x})

x \to 0 lim (\frac{x ^{2} - 1}{x - 1})

\int (2 x + 2) e^{- 2 x} d x

\int_{1}^{e} \frac{ln ( t )}{t} d t

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