Calculus Examples

$lim_{x \to \infty} \frac{10}{6 x}$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $10$ and $6$ .

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Step 1.1.1

Factor $2$ out of $10$ .

$lim_{x \to \infty} \frac{2 (5)}{6 x}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $6 x$ .

$lim_{x \to \infty} \frac{2 (5)}{2 (3 x)}$

Step 1.1.2.2

Cancel the common factor.

$lim_{x \to \infty} \frac{2 \cdot 5}{2 (3 x)}$

Step 1.1.2.3

Rewrite the expression.

$lim_{x \to \infty} \frac{5}{3 x}$

Step 1.2

Move the term $\frac{5}{3}$ outside of the limit because it is constant with respect to $x$ .

$\frac{5}{3} lim_{x \to \infty} \frac{1}{x}$

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x}$ approaches $0$ .

$\frac{5}{3} \cdot 0$

Step 3

Multiply $\frac{5}{3}$ by $0$ .

$0$