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

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

Popular >

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

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

\infty

Solution steps

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

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

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

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

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

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

\int_{- 1}^{3} 3 x^{2} d x

f (x) = I n (x)

x \to \infty lim (3 - \frac{1}{x})

\int x^{2} sin (7 x) d x

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