What is the limit as x approaches pi of tan(x/3) ?

The limit as x approaches pi of tan(x/3) is square root of 3

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limit as x approaches pi of tan(x/3)

x \to π lim (tan (\frac{x}{3}))

3

Decimal

1.73205 \dots

Solution steps

x \to π lim (tan (\frac{x}{3}))

Plug in the value

x = π

= tan (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

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}

= 3

\int_{0}^{2} \frac{x}{1 + x ^{2}} d x

x \to 9 lim (\frac{x - 3}{x - 9})

25 x^{2}, 9

(6.2) (9.3)

n = 1 \sum \infty (cos (2.8))^{n}

What is the limit as x approaches pi of tan(x/3) ?
The limit as x approaches pi of tan(x/3) is square root of 3