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

The limit as x approaches pi/2 of csc(x) is 1

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limit as x approaches pi/2 of csc(x)

x \to \frac{π}{2} lim (csc (x))

1

Solution steps

x \to \frac{π}{2} lim (csc (x))

Plug in the value

x = \frac{π}{2}

= csc (\frac{π}{2})

Use the following trivial identity:

csc (\frac{π}{2}) = 1

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 1

y = x - 1, (10, 3)

f (x) = 2 e^{0}

\int \frac{1}{cos ^{2} ( x ) 1 + tan ( x )} d x

\frac{\partial}{\partial x} (\frac{9 x}{y})

y = x x, (9, 27)

What is the limit as x approaches pi/2 of csc(x) ?
The limit as x approaches pi/2 of csc(x) is 1