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

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

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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

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

x \to 0 lim (3 x^{2} - 5 x + 3)

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

x \to 0 lim (11)

x \to 1 lim (x^{x})

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