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

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

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limit as x approaches 0+of x^2*ln(x)

x \to 0 + lim (x^{2} \cdot 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

q^{^{''}} + 40 q^{^{'}} + 4000 q = 0

\int \frac{17 x - 3}{3 x ^{2} + x - 2} d x

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\int \frac{5 - 4 x ^{2}}{3 + 2 x} d x

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