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Beliebt Rechnen >

limit as (x,y) approaches (0,0) of (sin(xy))/(sqrt(x^2+y^2))

Lösung

(x, y) \to (0, 0) lim (\frac{sin ( x y )}{x ^{2} + y ^{2}})

Lösung

0

Schritte zur Lösung

(x, y) \to (0, 0) lim (\frac{sin ( x y )}{x ^{2} + y ^{2}})

Schreibe in Polarkoordinaten um

x = r cos (θ)

= r \to 0 lim \frac{sin ( r cos ( θ ) r sin ( θ ) )}{( r cos ( θ ) ) ^{2} + ( r sin ( θ ) ) ^{2}}

Wenn

x \to a - lim f (x) = x \to a + lim f (x) = L

dann

x \to a lim f (x) = L

r \to 0 - lim \frac{sin ( r cos ( θ ) r sin ( θ ) )}{( r cos ( θ ) ) ^{2} + ( r sin ( θ ) ) ^{2}} = 0

r \to 0 + lim \frac{sin ( r cos ( θ ) r sin ( θ ) )}{( r cos ( θ ) ) ^{2} + ( r sin ( θ ) ) ^{2}} = 0

= 0

Beliebte Beispiele

integral from-2 to 2 of (32-8y^2)

\int_{- 2}^{2} (32 - 8 y^{2}) d y

derivative of ((3x-4/(5x+2))^{-5})

\frac{d}{d x} ((\frac{3 x - 4}{5 x + 2})^{- 5})

derivative f(x)=5x^2cos(x)+4x

d er i v a t i v e f (x) = 5 x^{2} cos (x) + 4 x

derivative 3x+sin(5x)

d er i v a t i v e 3 x + sin (5 x)

f(x)=ln(cos(x))

f (x) = ln (cos (x))