Calculus Examples

$lim_{x \to 4} x^{2} + 3 x - 1$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4} x^{2} + lim_{x \to 4} 3 x - lim_{x \to 4} 1$

Step 2

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

${(lim_{x \to 4} x)}^{2} + lim_{x \to 4} 3 x - lim_{x \to 4} 1$

Step 3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

${(lim_{x \to 4} x)}^{2} + 3 lim_{x \to 4} x - lim_{x \to 4} 1$

Step 4

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

${(lim_{x \to 4} x)}^{2} + 3 lim_{x \to 4} x - 1 \cdot 1$

Step 5

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4^{2} + 3 lim_{x \to 4} x - 1 \cdot 1$

Step 5.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$4^{2} + 3 \cdot 4 - 1 \cdot 1$

Step 6

Simplify the answer.

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Step 6.1

Simplify each term.

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Step 6.1.1

Raise $4$ to the power of $2$ .

$16 + 3 \cdot 4 - 1 \cdot 1$

Step 6.1.2

Multiply $3$ by $4$ .

$16 + 12 - 1 \cdot 1$

Step 6.1.3

Multiply $- 1$ by $1$ .

$16 + 12 - 1$

Step 6.2

Add $16$ and $12$ .

$28 - 1$

Step 6.3

Subtract $1$ from $28$ .

$27$