What is the limit as x approaches 0+of 3ln(x)+5/x ?

The limit as x approaches 0+of 3ln(x)+5/x is infinity

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limit as x approaches 0+of 3ln(x)+5/x

x \to 0 + lim (3 ln (x) + \frac{5}{x})

\infty

Solution steps

x \to 0 + lim (3 ln (x) + \frac{5}{x})

Simplify

3 ln (x) + \frac{5}{x} : \frac{3 x ln ( x ) + 5}{x}

= x \to 0 + lim (\frac{3 x ln ( x ) + 5}{x})

\frac{3 x ln ( x ) + 5}{x} = (3 x ln (x) + 5) \frac{1}{x}

= x \to 0 + lim ((3 x ln (x) + 5) \frac{1}{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 0 + lim (3 x ln (x) + 5) \cdot x \to 0 + lim (\frac{1}{x})

x \to 0 + lim (3 x ln (x) + 5) = 5

x \to 0 + lim (\frac{1}{x}) = \infty

= 5 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

What is the limit as x approaches 0+of 3ln(x)+5/x ?
The limit as x approaches 0+of 3ln(x)+5/x is infinity