limit as x approaches pi/2 of (cos^2(x))/((sin(1/2)x-cos(1/2)x)^2)

Lösung

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

0

Schritte zur Lösung

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

Setze den Wert

x = \frac{π}{2}

ein

= \frac{cos ^{2} ( \frac{π}{2} )}{( sin ( \frac{1}{2} ) \frac{π}{2} - cos ( \frac{1}{2} ) \frac{π}{2} ) ^{2}}

Vereinfache

\frac{cos ^{2} ( \frac{π}{2} )}{( sin ( \frac{1}{2} ) \frac{π}{2} - cos ( \frac{1}{2} ) \frac{π}{2} ) ^{2}} : 0

= 0

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