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

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

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Plug in the value

x = 0

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

Use the following trivial identity:

cos (0) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{3}

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