What is the limit as x approaches 2 of (sin(pix))/(x^2-4) ?

The limit as x approaches 2 of (sin(pix))/(x^2-4) is pi/4

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limit as x approaches 2 of (sin(pix))/(x^2-4)

x \to 2 lim (\frac{sin ( π x )}{x ^{2} - 4})

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

x \to 2 lim (\frac{sin ( π x )}{x ^{2} - 4})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 2

= \frac{cos ( π 2 ) π}{2 \cdot 2}

Simplify

\frac{cos ( π 2 ) π}{2 \cdot 2} : \frac{π}{4}

= \frac{π}{4}

x \to - \infty lim (\frac{4 x ^{2} + 1}{3 x - 1})

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

x \to \infty lim ((2 + x)^{\frac{1}{x}})

x \to 3 + lim (\frac{1 - x}{x - 3})

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

What is the limit as x approaches 2 of (sin(pix))/(x^2-4) ?
The limit as x approaches 2 of (sin(pix))/(x^2-4) is pi/4