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

The limit as x approaches pi of sec(x) is -1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches pi of sec(x)

x \to π lim (sec (x))

- 1

Solution steps

x \to π lim (sec (x))

Plug in the value

x = π

= sec (π)

Use the following trivial identity:

sec (π) = (- 1)

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}

= - 1

\int \frac{( 2 x + 4 )}{x ^{2} + 5 x - 6} d x

\int \frac{1}{t ^{2} - 6 t + 25} d t

\frac{d}{d x} (cos (ln (3 x)))

\int x - x d x

2 - x^{2}, - x

What is the limit as x approaches pi of sec(x) ?
The limit as x approaches pi of sec(x) is -1