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

The limit as x approaches 2 of (2x-1)^2-x^2 is 5

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limit as x approaches 2 of (2x-1)^2-x^2

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

5

Solution steps

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

Plug in the value

x = 2

= (2 \cdot 2 - 1)^{2} - 2^{2}

Simplify

(2 \cdot 2 - 1)^{2} - 2^{2} : 5

= 5

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What is the limit as x approaches 2 of (2x-1)^2-x^2 ?
The limit as x approaches 2 of (2x-1)^2-x^2 is 5