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

The limit as x approaches 3 of ((1+x)2-1)/x is 7/3

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

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

\frac{7}{3}

Decimal

2.33333 \dots

Solution steps

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

Plug in the value

x = 3

= \frac{( 1 + 3 ) \cdot 2 - 1}{3}

Simplify

= \frac{7}{3}

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

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

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

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

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

What is the limit as x approaches 3 of ((1+x)2-1)/x ?
The limit as x approaches 3 of ((1+x)2-1)/x is 7/3