Calculus Examples

$lim_{x \to 1} \frac{2 + 4 x}{3} = 2$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $\frac{1}{3}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{3} lim_{x \to 1} 2 + 4 x = 2$

Step 1.2

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

$\frac{1}{3} (lim_{x \to 1} 2 + lim_{x \to 1} 4 x) = 2$

Step 1.3

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

$\frac{1}{3} (2 + lim_{x \to 1} 4 x) = 2$

Step 1.4

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{3} (2 + 4 lim_{x \to 1} x) = 2$

Step 2

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

$\frac{1}{3} (2 + 4 \cdot 1) = 2$

Step 3

Simplify the answer.

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Step 3.1

Multiply $4$ by $1$ .

$\frac{1}{3} (2 + 4) = 2$

Step 3.2

Add $2$ and $4$ .

$\frac{1}{3} \cdot 6 = 2$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Factor $3$ out of $6$ .

$\frac{1}{3} \cdot (3 (2)) = 2$

Step 3.3.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 2) = 2$

Step 3.3.3

Rewrite the expression.

$2 = 2$