What is the limit as x approaches 3 of ((e^x-1)^2)/x ?

The limit as x approaches 3 of ((e^x-1)^2)/x is ((e^3-1)^2)/3

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limit as x approaches 3 of ((e^x-1)^2)/x

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

\frac{( e ^{3} - 1 ) ^{2}}{3}

Decimal Notation

121.41923 \dots

Solution steps

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

Plug in the value

x = 3

= \frac{( e ^{3} - 1 ) ^{2}}{3}

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

x \to 3 lim (4 x - 2 x - 5)

x \to 3 lim (2 e^{x})

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

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

What is the limit as x approaches 3 of ((e^x-1)^2)/x ?
The limit as x approaches 3 of ((e^x-1)^2)/x is ((e^3-1)^2)/3