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

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

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

x \to \frac{π}{4} lim (tan (x))

1

Solution steps

x \to \frac{π}{4} lim (tan (x))

Plug in the value

x = \frac{π}{4}

= tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

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