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

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

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

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

- π

Decimal Notation

- 3.14159 \dots

Solution steps

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

Simplify

\frac{sin ( - π x )}{2 + x} : - \frac{sin ( π x )}{2 + x}

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Apply L'Hopital's Rule

: x \to - 2 lim (\frac{cos ( π x ) π}{1})

= - x \to - 2 lim (\frac{cos ( π x ) π}{1})

Plug in the value

x = - 2

= - \frac{cos ( π ( - 2 ) ) π}{1}

Simplify

- \frac{cos ( π ( - 2 ) ) π}{1} : - π

= - π

\int_{2}^{3} \frac{22}{3 - x} d x

f (x) = x^{3} - 4 x, at x = 0

\frac{2}{( s + 2 )}

ln (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

x^{\frac{11}{2}}

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