What is the limit as x approaches 2 of sqrt(x^2-4x+1) ?

The limit as x approaches 2 of sqrt(x^2-4x+1) is sqrt(3)i

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limit as x approaches 2 of sqrt(x^2-4x+1)

x \to 2 lim (x^{2} - 4 x + 1)

3 i

Solution steps

x \to 2 lim (x^{2} - 4 x + 1)

Plug in the value

x = 2

= 2^{2} - 4 \cdot 2 + 1

Simplify

2^{2} - 4 \cdot 2 + 1 : 3 i

= 3 i

x \to 16 lim (\frac{x ^{3} - 2 x ^{2} - 3 x}{x + 5 - 2})

x \to 5 lim (\frac{x ^{2} - 5 x}{x - 10})

x \to \frac{x}{2} lim (\frac{( sin ( x ) - 1 )}{cos ( x )})

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

x \to - 1 lim (2 x^{2} - 5 x + 3 x)

What is the limit as x approaches 2 of sqrt(x^2-4x+1) ?
The limit as x approaches 2 of sqrt(x^2-4x+1) is sqrt(3)i