Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

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

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

Step 1.2

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

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

Step 2

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

$3 \cdot 0 - lim_{x \to \infty} 2$

Step 3

Evaluate the limit.

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Step 3.1

Evaluate the limit of $2$ which is constant as $x$ approaches $\infty$ .

$3 \cdot 0 - 1 \cdot 2$

Step 3.2

Simplify the answer.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Multiply $3$ by $0$ .

$0 - 1 \cdot 2$

Step 3.2.1.2

Multiply $- 1$ by $2$ .

$0 - 2$

Step 3.2.2

Subtract $2$ from $0$ .

$- 2$