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

The limit as x approaches pi+of cos(x) is -1

limit as x approaches pi+of cos(x)

x \to π + lim (cos (x))

- 1

Solution steps

x \to π + lim (cos (x))

Plug in the value

x = π

= cos (π)

Use the following trivial identity:

cos (π) = (- 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}

= - 1

u \to - 2 lim (\frac{u ^{3} + 4 u ^{2} + 4 u}{( u + 2 ) ( u - 3 )})

x \to 4 lim (\frac{x ^{2} - 3 x - 4}{x ^{2} - 8 x + 16})

x \to 7 + lim (\frac{x ^{2} - 4 x - 21}{∣ x - 7 ∣})

x \to 5 - lim (arcsin (\frac{x}{5}))

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

What is the limit as x approaches pi+of cos(x) ?
The limit as x approaches pi+of cos(x) is -1