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

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

Popular >

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

x \to 0 + lim (2 x (ln (x)))

0

Solution steps

x \to 0 + lim (2 x ln (x))

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

= 2 \cdot x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= 2 \cdot 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}}})

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

Simplify

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

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

Plug in the value

x = 0

= 2 (- 0)

Simplify

= 0

x \to + 3 lim (\frac{5}{x - 3})

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

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

x \to - 2 - lim (\frac{∣ x + 2 ∣}{x + 2})

x \to 1 lim (\frac{ln ( x )}{e ^{x}})

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