Calculus Examples

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

Step 1

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

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

Step 2

Evaluate the limit.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

${(- 1)}^{2} + 1$

Step 4

Simplify the answer.

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Step 4.1

Raise $- 1$ to the power of $2$ .

$1 + 1$

Step 4.2

Add $1$ and $1$ .

$2$