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

The limit as x approaches 0 of cos(pi) is -1

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limit as x approaches 0 of cos(pi)

x \to 0 lim (cos (π))

- 1

Solution steps

x \to 0 lim (cos (π))

x \to a lim c = c

= 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 + y = 10, (2, 8)

\int \frac{2 x ^{3} + x - 1}{x ^{3} + x ^{2} - 4 x - 4} d x

\int (16 x + 3) 8 x^{2} + 3 x d x

\frac{d}{d x} ((x - 2) (2 x + 3))

y = \frac{5 x}{1 + x ^{2}}, (4, \frac{20}{17})

What is the limit as x approaches 0 of cos(pi) ?
The limit as x approaches 0 of cos(pi) is -1