f(x)

(T)

x

Déplacer le curseur a vers 2, cela modifie la valeur de x vers 2

La \space  pente \space  de \space  la \space  droite \space  (AM) \space  est \space \space tan\theta = \frac{f(x)-f(2)}{x-2}

p = 1.3 (slider from 0.5 to 5, step 0.1)
f(x) = ((p * (x + 2)^(2)) * 1 / 8)
a = 3.7201 (slider from 2.0001 to 6, step 0.01)
M: (a, f(a))
A: (2, f(2))
b = Line(A, M)
c = OrthogonalLine(M, xAxis)
d = OrthogonalLine(A, yAxis)
B = Intersect(c, d)
e = Segment(B, M)
g = Segment(B, A)
θ = Angle(B, A, M)
BM = Distance(B, M)
AB = Distance(A, B)
tanα: BM / AB
h = OrthogonalLine(M, yAxis)
C = Intersect(h, yAxis)
i = Segment(C, M)
j = Tangent(2, f)
D = Intersect(c, xAxis)
k = Segment(D, B)
E = Point(xAxis)
l = OrthogonalLine(E, xAxis)
Q = Intersect(j, l)
m = OrthogonalLine(Q, yAxis)
P = Intersect(d, l)
H = Intersect(m, yAxis)
n = Segment(H, Q)
q = Segment(E, Q)
o: f'(2)
texte5: "Lorsque \space x  \space tend  \space vers \space  2,  \space  \space la \space  pente \space  de  \space la  \space droite  \space (AM) \space  tend  \space vers  \space \lim_{ x \to 2 }\frac{f(x)-f(2)}{x-2}=" + (LaTeX[o]) + ""
r = Segment(P, Q)
s = Segment(A, P)
t: r / s
texte2: "La \space  pente \space  de \space  la \space  droite  \space (T)  \space est \space  \frac{PQ}{AP}=" + (LaTeX[t]) + ""