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

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

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

x \to 0 lim (cos (\frac{π}{2}))

0

Solution steps

x \to 0 lim (cos (\frac{π}{2}))

x \to a lim c = c

= 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

y = 8 e^{x} cos (x)

\int \frac{( x + 1 )}{x} d x

\int \frac{1}{e ^{2 x} + 1} d x

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (x), y (0) = 1, y^{^{'}} (0) = - 1

y^{^{'}} = x + y, y (0) = 7

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