What is the limit as x approaches 0+of 1/x+ln(x) ?

The limit as x approaches 0+of 1/x+ln(x) is infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0+of 1/x+ln(x)

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

\infty

Solution steps

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

Factor out

\frac{1}{x}

from

\frac{1}{x} + ln (x) : \frac{1}{x} (1 + \frac{ln ( x )}{\frac{1}{x}})

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

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

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

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

(x^{2} + 2 y^{2}) d x = - x y d y

\int x ln (2 x) d x

\frac{sec ( x )}{x}

\frac{d y}{d x} = e^{x + y}

\frac{d}{d x} (ln (6 x - 5))

What is the limit as x approaches 0+of 1/x+ln(x) ?
The limit as x approaches 0+of 1/x+ln(x) is infinity