Simplify limit as x approaches 1 of x^2-2x+4

$lim_{x \to 1} x^{2} - 2 x + 4$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} x^{2} - lim_{x \to 1} 2 x + lim_{x \to 1} 4$

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

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

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

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

Evaluate the limit of $4$ which is constant as $x$ approaches $1$ .

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

Simplify terms.

Simplify each term.

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$1^{2} - 2 lim_{x \to 1} x + 4$

One to any power is one.

$1 - 2 lim_{x \to 1} x + 4$

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$1 - 2 \cdot 1 + 4$

Multiply $- 2$ by $1$ .

$1 - 2 + 4$

Simplify by adding and subtracting.

Subtract $2$ from $1$ .

$- 1 + 4$

Add $- 1$ and $4$ .

$3$