What is the limit as x approaches pi of (sin(x))/(1-\frac{x^2){pi^2}} ?

The limit as x approaches pi of (sin(x))/(1-\frac{x^2){pi^2}} is pi/2

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limit as x approaches pi of (sin(x))/(1-\frac{x^2){pi^2}}

x \to π lim (\frac{sin ( x )}{1 - \frac{x ^{2}}{π ^{2}}})

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

x \to π lim (\frac{sin ( x )}{1 - \frac{x ^{2}}{π ^{2}}})

Apply L'Hopital's Rule

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

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

Plug in the value

x = π

= \frac{cos ( π )}{- \frac{2 π}{π ^{2}}}

Simplify

\frac{cos ( π )}{- \frac{2 π}{π ^{2}}} : \frac{π}{2}

= \frac{π}{2}

x \to \infty lim (9 x^{2} e^{- x})

(\frac{x ^{3}}{6} + \frac{1}{2 x})^{^{'}}

\int_{6}^{\infty} \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x

\int_{0}^{5} x^{2} + 25 d x

y = sin (x y)

What is the limit as x approaches pi of (sin(x))/(1-\frac{x^2){pi^2}} ?
The limit as x approaches pi of (sin(x))/(1-\frac{x^2){pi^2}} is pi/2