Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Rewrite the expression.

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

Step 1.2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $- \infty$ .

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

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- \infty$ .

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

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{x^{2}}$ approaches $0$ .

$\frac{0 - lim_{x \to - \infty} \frac{1}{x}}{lim_{x \to - \infty} 1}$

Step 3

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

$\frac{0 - 0}{lim_{x \to - \infty} 1}$

Step 4

Evaluate the limit.

Tap for more steps...

Step 4.1

Evaluate the limit of $1$ which is constant as $x$ approaches $- \infty$ .

$\frac{0 - 0}{1}$

Step 4.2

Simplify the answer.

Tap for more steps...

Step 4.2.1

Divide $0 - 0$ by $1$ .

$0 - 0$

Step 4.2.2

Subtract $0$ from $0$ .

$0$