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

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

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limit as x approaches 0 of-cos(x)

x \to 0 lim (- cos (x))

- 1

Solution steps

x \to 0 lim (- cos (x))

Plug in the value

x = 0

= - cos (0)

Use the following trivial identity:

cos (0) = 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

\int 6 x - x^{2} d x

\frac{d}{d x} (3 x^{2} - 2 x - 8)

y d x + (x - 8) d y = 0, y (9) = 36

\int \frac{1}{x ( 1 - x ) ^{2}} d x

(x + 1) \frac{d y}{d x} = - y + 10

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