What is the limit as x approaches 3 of ((9-x^2))/(cos(pi/2 x)) ?

The limit as x approaches 3 of ((9-x^2))/(cos(pi/2 x)) is -(12)/pi

Popular >

limit as x approaches 3 of ((9-x^2))/(cos(pi/2 x))

x \to 3 lim (\frac{( 9 - x ^{2} )}{cos ( \frac{π}{2} x )})

- \frac{12}{π}

Decimal

- 3.81971 \dots

Solution steps

x \to 3 lim (\frac{9 - x ^{2}}{cos ( \frac{π}{2} x )})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 3

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

Simplify

\frac{- 2 \cdot 3}{- sin ( \frac{π 3}{2} ) \frac{π}{2}} : - \frac{12}{π}

= - \frac{12}{π}

n = 0 \sum \infty (- 1)^{2 n + 1}

\int sin^{2} (θ) cos^{2} (θ) d θ

\int \frac{1}{1 + 6 x} d x

\frac{d}{d x} ((x^{2} + 2)^{2} (x^{4} + 4)^{4})

5 x y \frac{d y}{d x} = 3

What is the limit as x approaches 3 of ((9-x^2))/(cos(pi/2 x)) ?
The limit as x approaches 3 of ((9-x^2))/(cos(pi/2 x)) is -(12)/pi