What is the limit as x approaches 3 of ((1+ln(x)))/x ?

The limit as x approaches 3 of ((1+ln(x)))/x is (1+ln(3))/3

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limit as x approaches 3 of ((1+ln(x)))/x

x \to 3 lim (\frac{( 1 + ln ( x ) )}{x})

\frac{1 + ln ( 3 )}{3}

Decimal Notation

0.69953 \dots

Solution steps

x \to 3 lim (\frac{1 + ln ( x )}{x})

Plug in the value

x = 3

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

x \to 3 lim (\frac{( 1 + x ) 2 - 1}{x})

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

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

x \to 3 lim (\frac{5}{x ^{2}})

x \to 3 lim (3 x^{2} + 6 x + 5)

What is the limit as x approaches 3 of ((1+ln(x)))/x ?
The limit as x approaches 3 of ((1+ln(x)))/x is (1+ln(3))/3