What is the limit as x approaches 0 of (cos(3x))/(x+3) ?

The limit as x approaches 0 of (cos(3x))/(x+3) is 1/3

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limit as x approaches 0 of (cos(3x))/(x+3)

x \to 0 lim (\frac{cos ( 3 x )}{x + 3})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 0 lim (\frac{cos ( 3 x )}{x + 3})

Plug in the value

x = 0

= \frac{cos ( 3 \cdot 0 )}{0 + 3}

Simplify

\frac{cos ( 3 \cdot 0 )}{0 + 3} : \frac{1}{3}

= \frac{1}{3}

What is the limit as x approaches 0 of (cos(3x))/(x+3) ?
The limit as x approaches 0 of (cos(3x))/(x+3) is 1/3