What is the limit as x approaches pi/6 of cos(x) ?

The limit as x approaches pi/6 of cos(x) is (sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches pi/6 of cos(x)

x \to \frac{π}{6} lim (cos (x))

\frac{3}{2}

Decimal

0.86602 \dots

Solution steps

x \to \frac{π}{6} lim (cos (x))

Plug in the value

x = \frac{π}{6}

= cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

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{3}{2}

t \to 1 lim (t + 2)

\frac{d}{d x} (\frac{1}{cot ( x )})

\frac{d}{d x} ((- 4 x^{2} + 9)^{2})

\frac{d}{d y} (x cos (x) y)

\int \frac{( sin ^{2} ( x ) )}{x ^{2}} d x

What is the limit as x approaches pi/6 of cos(x) ?
The limit as x approaches pi/6 of cos(x) is (sqrt(3))/2