Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 2$ .

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

Step 1.2

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

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

Step 1.3

Evaluate the limit of $2 t$ which is constant as $x$ approaches $- 2$ .

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

Step 1.4

Evaluate the limit of $1$ which is constant as $x$ approaches $- 2$ .

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

Step 2

Evaluate the limit of $x$ by plugging in $- 2$ for $x$ .

${(- 2)}^{2} + 2 t - 1 \cdot 1$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

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

$4 + 2 t - 1 \cdot 1$

Step 3.1.2

Multiply $- 1$ by $1$ .

$4 + 2 t - 1$

Step 3.2

Subtract $1$ from $4$ .

$2 t + 3$