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

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

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

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

0

Solution steps

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Simplify

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

= x \to 0 + lim (- 2 x)

Plug in the value

x = 0

= - 2 \cdot 0

Simplify

= 0

x \to 4 lim (- 12 x^{2} + 72 x - 60)

n \to 0 lim (\frac{n}{n + 1})

x \to \infty lim (\frac{cos ( 24 x )}{24 x})

x \to - 1 lim (x - 1)

x \to 1 lim (x^{4} - 5 x^{3} - x - 1)

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