Calculus Examples

$lim_{x \to 0} - \frac{5}{2} \cdot (10 x - 20)$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $- \frac{5}{2}$ outside of the limit because it is constant with respect to $x$ .

$- \frac{5}{2} lim_{x \to 0} 10 x - 20$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$- \frac{5}{2} (lim_{x \to 0} 10 x - lim_{x \to 0} 20)$

Step 1.3

Move the term $10$ outside of the limit because it is constant with respect to $x$ .

$- \frac{5}{2} (10 lim_{x \to 0} x - lim_{x \to 0} 20)$

Step 1.4

Evaluate the limit of $20$ which is constant as $x$ approaches $0$ .

$- \frac{5}{2} (10 lim_{x \to 0} x - 1 \cdot 20)$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$- \frac{5}{2} (10 \cdot 0 - 1 \cdot 20)$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $10$ by $0$ .

$- \frac{5}{2} (0 - 1 \cdot 20)$

Step 3.1.2

Multiply $- 1$ by $20$ .

$- \frac{5}{2} (0 - 20)$

Step 3.2

Subtract $20$ from $0$ .

$- \frac{5}{2} \cdot - 20$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} \cdot - 20$

Step 3.3.2

Factor $2$ out of $- 20$ .

$\frac{- 5}{2} \cdot (2 (- 10))$

Step 3.3.3

Cancel the common factor.

$\frac{- 5}{2} \cdot (2 \cdot - 10)$

Step 3.3.4

Rewrite the expression.

$- 5 \cdot - 10$

Step 3.4

Multiply $- 5$ by $- 10$ .

$50$