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

The limit as x approaches pi/3 of sec(x) is 2

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

x \to \frac{π}{3} lim (sec (x))

2

Solution steps

x \to \frac{π}{3} lim (sec (x))

Plug in the value

x = \frac{π}{3}

= sec (\frac{π}{3})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (x)

periodicity table with

2 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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

x \to π lim (0.4)

y = tan (5 x^{3})

\frac{\partial}{\partial x} (x \cdot cos (x))

\frac{\partial}{\partial x} (x cos (y) sin (z))

y = 6 4 + x

What is the limit as x approaches pi/3 of sec(x) ?
The limit as x approaches pi/3 of sec(x) is 2