Calculus Examples

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

Step 1

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

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

Step 2

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

$0 + lim_{x \to \infty} 1$

Step 3

Evaluate the limit.

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Step 3.1

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

$0 + 1$

Step 3.2

Add $0$ and $1$ .

$1$