Calculus Examples

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

Step 1

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

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Step 1.1

Raise $x$ to the power of $1$ .

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

Step 1.2

Factor $x$ out of $x^{1}$ .

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

Step 1.3

Cancel the common factors.

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Step 1.3.1

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

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

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 $0$ .

$0$