Calculus Examples

$lim_{x \to \infty} 4 - \frac{3}{x^{2}}$

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 $\infty$ .

$lim_{x \to \infty} 4 - lim_{x \to \infty} \frac{3}{x^{2}}$

Step 1.2

Evaluate the limit of $4$ which is constant as $x$ approaches $\infty$ .

$4 - lim_{x \to \infty} \frac{3}{x^{2}}$

Step 1.3

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

$4 - 3 lim_{x \to \infty} \frac{1}{x^{2}}$

Step 2

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

$4 - 3 \cdot 0$

Step 3

Simplify the answer.

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Step 3.1

Multiply $- 3$ by $0$ .

$4 + 0$

Step 3.2

Add $4$ and $0$ .

$4$