Calculus Examples

$lim_{s \to \frac{2}{3}} 3 s (2 s - 1)$

Step 1

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

$3 lim_{s \to \frac{2}{3}} s (2 s - 1)$

Step 2

Evaluate the limits by plugging in $\frac{2}{3}$ for all occurrences of $s$ .

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Step 2.1

Evaluate the limit of $s (2 s - 1)$ by plugging in $\frac{2}{3}$ for $s$ .

$3 s (2 (\frac{2}{3}) - 1)$

Step 2.2

Multiply $2 (\frac{2}{3})$ .

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Step 2.2.1

Combine $2$ and $\frac{2}{3}$ .

$3 s (\frac{2 \cdot 2}{3} - 1)$

Step 2.2.2

Multiply $2$ by $2$ .

$3 s (\frac{4}{3} - 1)$

Step 2.3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$3 s (\frac{4}{3} - 1 \cdot \frac{3}{3})$

Step 2.4

Combine $- 1$ and $\frac{3}{3}$ .

$3 s (\frac{4}{3} + \frac{- 1 \cdot 3}{3})$

Step 2.5

Combine the numerators over the common denominator.

$3 s (\frac{4 - 1 \cdot 3}{3})$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 1$ by $3$ .

$3 s (\frac{4 - 3}{3})$

Step 2.6.2

Subtract $3$ from $4$ .

$3 s (\frac{1}{3})$