What is the limit as x approaches pi/4 of cos(x) ?

The limit as x approaches pi/4 of cos(x) is (sqrt(2))/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/4 of cos(x)

x \to \frac{π}{4} lim (cos (x))

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

x \to \frac{π}{4} lim (cos (x))

Plug in the value

x = \frac{π}{4}

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{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{2}{2}

x \to 1 + lim (ln (\frac{1}{x - 1}))

x \to 2 lim (\frac{3 x + 1}{2 - x})

x \to 2 lim (x)

x \to 0 lim (\frac{1 - sec ( x )}{2 x})

x \to 1 lim (\frac{∣ 1 - x ∣}{x - 1})

What is the limit as x approaches pi/4 of cos(x) ?
The limit as x approaches pi/4 of cos(x) is (sqrt(2))/2