What is the limit as x approaches pi/3 of 1/(sec(x)) ?

The limit as x approaches pi/3 of 1/(sec(x)) is 1/2

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limit as x approaches pi/3 of 1/(sec(x))

x \to \frac{π}{3} lim (\frac{1}{sec ( x )})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to \frac{π}{3} lim (\frac{1}{sec ( x )})

Plug in the value

x = \frac{π}{3}

= \frac{1}{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}

= \frac{1}{2}

\frac{d y}{cos ( x ) + y} = d x

\int_{0}^{1} sin^{2} (π x) d x

\frac{\partial}{\partial x} (arctan (x + 2 y))

\int \frac{1}{x} ln (x^{2}) d x

x \to 18 lim (\frac{1}{x - 18})

What is the limit as x approaches pi/3 of 1/(sec(x)) ?
The limit as x approaches pi/3 of 1/(sec(x)) is 1/2