tangent 4/(x^2)-1/(sqrt(x))

Lösung

tangente von

\frac{4}{x ^{2}} - \frac{1}{x}

y = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}} x + \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}} - \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{7}{2}}}

Schritte zur Lösung

Berechne den Graphen der Tangente für den allgemeinen Punkt

x = a_{0}

Finde den Tangentenpunkt:

(a_{0}, \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}})

Finde die Steigung von

y = \frac{4}{x ^{2}} - \frac{1}{x} : \frac{d y}{d x} = \frac{- 16 x ^{\frac{3}{2}} + x ^{3}}{2 x ^{\frac{9}{2}}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}}

Finde den Graphen mit Steigung m=

\frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}}

, der durch den Punkt

(a_{0}, \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}})

verläuft:

y = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}} x + \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}} - \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{7}{2}}}

y = \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{9}{2}}} x + \frac{4 - a _{0}^{\frac{3}{2}}}{a _{0}^{\frac{3}{2}} a _{0}} - \frac{- 16 a _{0}^{\frac{3}{2}} + a _{0}^{3}}{2 a _{0}^{\frac{7}{2}}}

\frac{d ^{2}}{d x ^{2}} (\frac{1}{1 - x ^{2}})

\int 2 y arctan (x) d y

\int \frac{6}{sec ( 2 x ) - 1} d x

\int (a - b y)^{4} d y

x \to 5 + lim (x^{2} + 2 x - 3)