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 5

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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})

5

Solution steps

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

Plug in the value

x = 3

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

Simplify

= 5

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

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

x \to 3 lim (3 x^{2} - 5 x + 8)

x \to 3 lim (ln (x) ln (1 + x))

x \to 3 lim (\frac{1}{( x ln ( 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 5