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

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

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limit as x approaches 3 of ln(e^x+1)

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

ln (e^{3} + 1)

Decimal Notation

3.04858 \dots

Solution steps

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

Plug in the value

x = 3

= ln (e^{3} + 1)

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

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

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

x \to 3 lim (\frac{3}{x})

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

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