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

The limit as x approaches pi of cos(x/2) is 0

Popular >

limit as x approaches pi of cos(x/2)

x \to π lim (cos (\frac{x}{2}))

0

Solution steps

x \to π lim (cos (\frac{x}{2}))

Plug in the value

x = π

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

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}

= 0

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

x \to 5 lim (\frac{3 x - 2}{x - 5})

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

x \to - 2 lim (- x^{4} + 8 x^{2})

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

What is the limit as x approaches pi of cos(x/2) ?
The limit as x approaches pi of cos(x/2) is 0