Calculus Examples

$lim_{x \to \infty} \frac{x^{2}}{x^{3}}$

Step 1

Cancel the common factor of $x^{2}$ and $x^{3}$ .

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Step 1.1

Multiply by $1$ .

$lim_{x \to \infty} \frac{x^{2} \cdot 1}{x^{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x^{2}$ out of $x^{3}$ .

$lim_{x \to \infty} \frac{x^{2} \cdot 1}{x^{2} x}$

Step 1.2.2

Cancel the common factor.

$lim_{x \to \infty} \frac{x^{2} \cdot 1}{x^{2} x}$

Step 1.2.3

Rewrite the expression.

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

Step 2

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

$0$