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

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

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

x \to \frac{π}{2} lim (\frac{sec ( x )}{sec ( 3 x )})

- 3

Solution steps

x \to \frac{π}{2} lim (\frac{sec ( x )}{sec ( 3 x )})

Express with sin, cos

= x \to \frac{π}{2} lim (\frac{cos ( 3 x )}{cos ( x )})

Apply L'Hopital's Rule

: x \to \frac{π}{2} lim (\frac{- sin ( 3 x ) \cdot 3}{- sin ( x )})

= x \to \frac{π}{2} lim (\frac{- sin ( 3 x ) \cdot 3}{- sin ( x )})

Plug in the value

x = \frac{π}{2}

= \frac{- sin ( 3 \cdot \frac{π}{2} ) \cdot 3}{- sin ( \frac{π}{2} )}

Simplify

\frac{- sin ( 3 \cdot \frac{π}{2} ) \cdot 3}{- sin ( \frac{π}{2} )} : - 3

= - 3

\int (x^{2} - 1)^{3} (2 x) d x

f (x) = 3 + 4 x^{2} - 2 x^{3}, at x = a

(y + 4) y^{^{'}} = 2 x y + 4 y, y (2) = 1

\int (1 + 30 w) w d w

\int 1 - x^{2} d x

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