What is the limit as x approaches 0-of x^2ln(-x) ?

The limit as x approaches 0-of x^2ln(-x) is 0

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limit as x approaches 0-of x^2ln(-x)

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

0

Solution steps

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

: x \to 0 - lim (\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}})

= x \to 0 - lim (\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}})

Simplify

\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}} : - \frac{x ^{2}}{2}

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

Plug in the value

x = 0

= - \frac{0 ^{2}}{2}

Simplify

- \frac{0 ^{2}}{2} : 0

= 0

x \to 0 + lim (x^{3} e^{\frac{1}{x}})

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

a \to 0 lim (cot (a) - csc (a))

x \to - 1 lim (\frac{3 x ^{2}}{2 x - 1})

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

What is the limit as x approaches 0-of x^2ln(-x) ?
The limit as x approaches 0-of x^2ln(-x) is 0