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

The limit as x approaches pi/2 of (sec(x))/(sec^2(3x)) is 0

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

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

0

Solution steps

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

Express with sin, cos

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

Apply L'Hopital's Rule

: x \to \frac{π}{2} lim (\frac{- 3 sin ( 6 x )}{- sin ( x )})

= x \to \frac{π}{2} lim (\frac{- 3 sin ( 6 x )}{- sin ( x )})

Plug in the value

x = \frac{π}{2}

= \frac{- 3 sin ( 6 \cdot \frac{π}{2} )}{- sin ( \frac{π}{2} )}

Simplify

\frac{- 3 sin ( 6 \cdot \frac{π}{2} )}{- sin ( \frac{π}{2} )} : 0

= 0

x \to 0 lim (x \cdot (sin (\frac{1}{x})))

x \to 2 lim (x^{3} + 5 x^{2} - 5 x + 3)

x \to 0 lim (\frac{ln ( cos ( 3 x ) )}{ln ( cos ( 5 x ) )})

h \to 0 lim (\frac{( 2 + h ) ^{5} - 32}{h})

x \to - \infty lim (x^{2 n})

What is the limit as x approaches pi/2 of (sec(x))/(sec^2(3x)) ?
The limit as x approaches pi/2 of (sec(x))/(sec^2(3x)) is 0