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

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

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limit as x approaches 0+of x*sin(ln(x))

x \to 0 + lim (x \cdot sin (ln (x)))

0

Solution steps

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

Apply the Squeeze Theorem:

0

= 0

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

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

x \to \infty lim (sin (2))

x \to 1 lim (x ln (sin (\frac{x}{2})))

x \to 3 lim (x^{2} - 6 x + 9)

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