What is the limit as t approaches pi of tan(t/6) ?

The limit as t approaches pi of tan(t/6) is (sqrt(3))/3

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limit as t approaches pi of tan(t/6)

t \to π lim (tan (\frac{t}{6}))

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

t \to π lim (tan (\frac{t}{6}))

Plug in the value

t = π

= tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{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}

= \frac{3}{3}

\int_{1}^{5} \frac{x ^{2} + 1}{6 x - x ^{2}} d x

\frac{d}{d x} (6 x^{2} - 8 + 40 cos (π) x)

\int \frac{x ^{3}}{1 + x ^{2}} d x

\frac{d}{d x} (\frac{2 x + 1}{x})

f (x) = \frac{( x + 1 )}{x - 1}

What is the limit as t approaches pi of tan(t/6) ?
The limit as t approaches pi of tan(t/6) is (sqrt(3))/3