Calculus Examples

$\frac{lim_{x \to i n f} x + \sin (x)}{x + \cos (x)}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $i n f$ .

$\frac{lim_{x \to i n f} x + lim_{x \to i n f} \sin (x)}{x + \cos (x)}$

Step 2

Move the limit inside the trig function because sine is continuous.

$\frac{lim_{x \to i n f} x + \sin (lim_{x \to i n f} x)}{x + \cos (x)}$

Step 3

Evaluate the limits by plugging in $i n f$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $i n f$ for $x$ .

$\frac{i n f + \sin (lim_{x \to i n f} x)}{x + \cos (x)}$

Step 3.2

Evaluate the limit of $x$ by plugging in $i n f$ for $x$ .

$\frac{i n f + \sin (i n f)}{x + \cos (x)}$