Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

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

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

Step 1.2

Move the term $\frac{1}{4}$ outside of the limit because it is constant with respect to $x$ .

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

Step 1.3

Evaluate the limit of $2$ which is constant as $x$ approaches $4$ .

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

Step 2

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

$- \frac{1}{4} \cdot 4 + 2$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{- 1}{4} \cdot 4 + 2$

Step 3.1.2

Cancel the common factor.

$\frac{- 1}{4} \cdot 4 + 2$

Step 3.1.3

Rewrite the expression.

$- 1 + 2$

Step 3.2

Add $- 1$ and $2$ .

$1$