limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi)

Lösung

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

\frac{1}{4}

Dezimale

0.25

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

= x \to \frac{π}{4} lim (\frac{cos ( x - \frac{π}{4} )}{4})

Setze den Wert

x = \frac{π}{4}

ein

= \frac{cos ( \frac{π}{4} - \frac{π}{4} )}{4}

cos (\frac{π}{4} - \frac{π}{4}) = 1

= \frac{1}{4}

x^{^{'}} + x = 0

\frac{1}{x} \frac{d y}{d x} = \frac{1}{x ^{2} + 1}

x \to 0 lim (\frac{x e ^{x}}{sin ( x )})

n = 1 \sum \infty 1 (\frac{5}{6})^{n}

k = 1 \sum \infty cos (\frac{1}{k}) - cos (\frac{1}{k + 1})