What is the limit as x approaches 0+of tan(xln(x)) ?

The limit as x approaches 0+of tan(xln(x)) is 0

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limit as x approaches 0+of tan(xln(x))

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

0

Solution steps

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

Express with sin, cos

= x \to 0 + lim (\frac{sin ( x ln ( x ) )}{cos ( x ln ( x ) )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to 0 +} ( sin ( x ln ( x ) ) )}{lim _{x \to 0 +} ( cos ( x ln ( x ) ) )}

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

x \to 0 + lim (cos (x ln (x))) = 1

= \frac{0}{1}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

What is the limit as x approaches 0+of tan(xln(x)) ?
The limit as x approaches 0+of tan(xln(x)) is 0