limit as x approaches infinity of 5e^{-t}i-(5t)/(t+7)j+5arctan(tk)

Lösung

x \to \infty lim (5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k))

\frac{5 arctan ( k t ) ( 7 + t ) - 5 j t}{7 + t} + 5 i e^{- t}

Schritte zur Lösung

x \to \infty lim (5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k))

x \to a lim c = c

= 5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k)

Vereinfache

5 e^{- t} i - \frac{5 t}{t + 7} j + 5 arctan (t k) : \frac{5 arctan ( k t ) ( 7 + t ) - 5 j t}{7 + t} + 5 i e^{- t}

= \frac{5 arctan ( k t ) ( 7 + t ) - 5 j t}{7 + t} + 5 i e^{- t}

\frac{\partial}{\partial x} (x^{2} + y^{2} + 3 x y + 5 x)

x^{2} y^{^{'}} + (2 - y) = 0

\frac{\partial}{\partial y} (2 x e^{- y})

\frac{\partial}{\partial x} (7 x y^{3} + 5)

t^{2} y^{^{'}} + 2 t y - y^{3} = 0