What is the limit as x approaches pi/4 of cot(x) ?

The limit as x approaches pi/4 of cot(x) is 1

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limit as x approaches pi/4 of cot(x)

x \to \frac{π}{4} lim (cot (x))

1

Solution steps

x \to \frac{π}{4} lim (cot (x))

Plug in the value

x = \frac{π}{4}

= cot (\frac{π}{4})

Use the following trivial identity:

cot (\frac{π}{4}) = 1

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

What is the limit as x approaches pi/4 of cot(x) ?
The limit as x approaches pi/4 of cot(x) is 1