What is the limit as x approaches 1+of (x^2)/(ln(x)) ?

The limit as x approaches 1+of (x^2)/(ln(x)) is infinity

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limit as x approaches 1+of (x^2)/(ln(x))

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

\infty

Solution steps

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

\frac{x ^{2}}{ln ( x )} = x^{2} \frac{1}{ln ( x )}

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

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

With the exception of indeterminate form

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

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

x \to 1 + lim (\frac{1}{ln ( x )}) = \infty

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 1 lim (- 8)

x \to \frac{π}{2} lim ((sin^{2} (x))^{t a n (x)})

x \to - 1 lim (7)

x \to - 3 lim (\frac{x ^{2} - 2}{x - 4})

x \to - 2 lim (3 x - 4 x^{2})

What is the limit as x approaches 1+of (x^2)/(ln(x)) ?
The limit as x approaches 1+of (x^2)/(ln(x)) is infinity