Calculus Examples

$\frac{lim_{x \to 0} (x) (2 x - 1)}{2 x + 1}$

Step 1

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

$\frac{lim_{x \to 0} x \cdot lim_{x \to 0} 2 x - 1}{2 x + 1}$

Step 2

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

$\frac{lim_{x \to 0} x \cdot (lim_{x \to 0} 2 x - lim_{x \to 0} 1)}{2 x + 1}$

Step 3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{lim_{x \to 0} x \cdot (2 lim_{x \to 0} x - lim_{x \to 0} 1)}{2 x + 1}$

Step 4

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$\frac{lim_{x \to 0} x \cdot (2 lim_{x \to 0} x - 1 \cdot 1)}{2 x + 1}$

Step 5

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 5.1

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

$\frac{0 \cdot (2 lim_{x \to 0} x - 1 \cdot 1)}{2 x + 1}$

Step 5.2

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

$\frac{0 \cdot (2 \cdot 0 - 1 \cdot 1)}{2 x + 1}$

Step 6

Simplify the answer.

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Step 6.1

Multiply $0$ by $2 \cdot 0 - 1 \cdot 1$ .

$\frac{0}{2 x + 1}$

Step 6.2

Divide $0$ by $2 x + 1$ .

$0$