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

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

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

x \to π lim (tan (\frac{x}{4}))

1

Solution steps

x \to π lim (tan (\frac{x}{4}))

Plug in the value

x = π

= 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

x \to 0 lim (x tan (\frac{π}{2} - x))

x \to 2 - lim (\frac{- 3}{x - 2})

x \to 0 lim (\frac{4 x - x ^{2}}{x})

x \to 0 lim (\frac{x}{2 x ^{2}})

x \to 0 + lim (\frac{e ^{1 + x} - e}{x})

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