Calculus Examples

$lim_{x \to - 1} 2 x^{2} + 6 x - 1$

Step 1

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

$lim_{x \to - 1} 2 x^{2} + lim_{x \to - 1} 6 x - lim_{x \to - 1} 1$

Step 2

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

$2 lim_{x \to - 1} x^{2} + lim_{x \to - 1} 6 x - lim_{x \to - 1} 1$

Step 3

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

$2 {(lim_{x \to - 1} x)}^{2} + lim_{x \to - 1} 6 x - lim_{x \to - 1} 1$

Step 4

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$2 {(lim_{x \to - 1} x)}^{2} + 6 lim_{x \to - 1} x - lim_{x \to - 1} 1$

Step 5

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

$2 {(lim_{x \to - 1} x)}^{2} + 6 lim_{x \to - 1} x - 1 \cdot 1$

Step 6

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

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Step 6.1

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

$2 {(- 1)}^{2} + 6 lim_{x \to - 1} x - 1 \cdot 1$

Step 6.2

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

$2 {(- 1)}^{2} + 6 \cdot - 1 - 1 \cdot 1$

Step 7

Simplify the answer.

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Step 7.1

Simplify each term.

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Step 7.1.1

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

$2 \cdot 1 + 6 \cdot - 1 - 1 \cdot 1$

Step 7.1.2

Multiply $2$ by $1$ .

$2 + 6 \cdot - 1 - 1 \cdot 1$

Step 7.1.3

Multiply $6$ by $- 1$ .

$2 - 6 - 1 \cdot 1$

Step 7.1.4

Multiply $- 1$ by $1$ .

$2 - 6 - 1$

Step 7.2

Subtract $6$ from $2$ .

$- 4 - 1$

Step 7.3

Subtract $1$ from $- 4$ .

$- 5$