Calculus Examples

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

Step 1

Change the two-sided limit into a right sided limit.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

Tap for more steps...

Step 6.1

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

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

Step 6.2

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

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

Step 7

Simplify the answer.

Tap for more steps...

Step 7.1

Simplify each term.

Tap for more steps...

Step 7.1.1

One to any power is one.

$1 - 2 \cdot 1 + 4$

Step 7.1.2

Multiply $- 2$ by $1$ .

$1 - 2 + 4$

Step 7.2

Subtract $2$ from $1$ .

$- 1 + 4$

Step 7.3

Add $- 1$ and $4$ .

$3$