Calculus Examples

$lim_{x \to x} \frac{x \cos (x)}{2 x}$

Step 1

Evaluate the limit.

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Step 1.1

Cancel the common factor of $x$ .

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Step 1.1.1

Cancel the common factor.

$lim_{x \to x} \frac{x \cos (x)}{2 x}$

Step 1.1.2

Rewrite the expression.

$lim_{x \to x} \frac{\cos (x)}{2}$

Step 1.2

Move the term $\frac{1}{2}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{2} lim_{x \to x} \cos (x)$

Step 1.3

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

$\frac{1}{2} \cos (lim_{x \to x} x)$

Step 2

Evaluate the limit of $x$ by plugging in $x$ for $x$ .

$\frac{1}{2} \cos (x)$

Step 3

Combine $\frac{1}{2}$ and $\cos (x)$ .

$\frac{\cos (x)}{2}$