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

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

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

x \to \frac{π}{2} - lim (cos (x))

0

Solution steps

x \to \frac{π}{2} - lim (cos (x))

Plug in the value

x = \frac{π}{2}

= 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

\frac{d y}{d x} = \frac{( 5 y ^{3} - 2 x y )}{x ^{2}}

(1 + cos^{2} (x))^{4}

y = x^{3} - 16 x^{2} + 45 x + 6

\int 4 sin (x) + 4 d x

\frac{d y}{d x} = \frac{1}{4} y

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