Ma4A_ChAv3_TaylorComplet

f(x)=

Polynome de Taylor d'ordre n :

f(x) = ℯ^(x)
InputBox1 = Textfield(f)
a = 0 (slider from -5 to 5, step 0.1)
n = 7 (slider from 1 to 30, step 1)
A1: 0
A2: A1 + 1
A3: A2 + 1
A4: A3 + 1
A5: A4 + 1
A6: A5 + 1
A7: A6 + 1
A8: A7 + 1
A9: A8 + 1
A10: A9 + 1
B2 = Derivative(f, A2)
B3 = Derivative(f, A3)
B4 = Derivative(f, A4)
B5 = Derivative(f, A5)
B6 = Derivative(f, A6)
B7 = Derivative(f, A7)
B8 = Derivative(f, A8)
B9 = Derivative(f, A9)
B10 = Derivative(f, A10)
C2(x) = (B2(a) * (x - a)^(A2) / A2!)
C3(x) = (B3(a) * (x - a)^(A3) / A3!)
C4(x) = (B4(a) * (x - a)^(A4) / A4!)
C5(x) = (B5(a) * (x - a)^(A5) / A5!)
C6(x) = (B6(a) * (x - a)^(A6) / A6!)
C7(x) = (B7(a) * (x - a)^(A7) / A7!)
C8(x) = (B8(a) * (x - a)^(A8) / A8!)
C9(x) = (B9(a) * (x - a)^(A9) / A9!)
C10(x) = (B10(a) * (x - a)^(A10) / A10!)
A11: A10 + 1
B11 = Derivative(f, A11)
C11(x) = (B11(a) * (x - a)^(A11) / A11!)
text1: "f(x)=" + (LaTeX[InputBox1]) + ""
x_0 = 1.2 (slider from -5 to 5, step 0.1)
A12: A11 + 1
B12 = Derivative(f, A12)
C12(x) = (B12(a) * (x - a)^(A12) / A12!)
A13: A12 + 1
B13 = Derivative(f, A13)
C13(x) = (B13(a) * (x - a)^(A13) / A13!)
A14: A13 + 1
B14 = Derivative(f, A14)
C14(x) = (B14(a) * (x - a)^(A14) / A14!)
A15: A14 + 1
B15 = Derivative(f, A15)
C15(x) = (B15(a) * (x - a)^(A15) / A15!)
A16: A15 + 1
B16 = Derivative(f, A16)
C16(x) = (B16(a) * (x - a)^(A16) / A16!)
A17: A16 + 1
B17 = Derivative(f, A17)
C17(x) = (B17(a) * (x - a)^(A17) / A17!)
A18: A17 + 1
B18 = Derivative(f, A18)
C18(x) = (B18(a) * (x - a)^(A18) / A18!)
A19: A18 + 1
B19 = Derivative(f, A19)
C19(x) = (B19(a) * (x - a)^(A19) / A19!)
A20: A19 + 1
B20 = Derivative(f, A20)
C20(x) = (B20(a) * (x - a)^(A20) / A20!)
A21: A20 + 1
B21 = Derivative(f, A21)
C21(x) = (B21(a) * (x - a)^(A21) / A21!)
A22: A21 + 1
B22 = Derivative(f, A22)
C22(x) = (B22(a) * (x - a)^(A22) / A22!)
A23: A22 + 1
B23 = Derivative(f, A23)
C23(x) = (B23(a) * (x - a)^(A23) / A23!)
A24: A23 + 1
B24 = Derivative(f, A24)
C24(x) = (B24(a) * (x - a)^(A24) / A24!)
A25: A24 + 1
B25 = Derivative(f, A25)
C25(x) = (B25(a) * (x - a)^(A25) / A25!)
A26: A25 + 1
B26 = Derivative(f, A26)
C26(x) = (B26(a) * (x - a)^(A26) / A26!)
A27: A26 + 1
B27 = Derivative(f, A27)
C27(x) = (B27(a) * (x - a)^(A27) / A27!)
A28: A27 + 1
B28 = Derivative(f, A28)
C28(x) = (B28(a) * (x - a)^(A28) / A28!)
A29: A28 + 1
B29 = Derivative(f, A29)
C29(x) = (B29(a) * (x - a)^(A29) / A29!)
A30: A29 + 1
B30 = Derivative(f, A30)
C30(x) = (B30(a) * (x - a)^(A30) / A30!)
A31: A30 + 1
B31 = Derivative(f, A31)
C31(x) = (B31(a) * (x - a)^(A31) / A31!)
A32: A31 + 1
B32 = Derivative(f, A32)
C32(x) = (B32(a) * (x - a)^(A32) / A32!)
A33: A32 + 1
B33 = Derivative(f, A33)
C33(x) = (B33(a) * (x - a)^(A33) / A33!)
A34: A33 + 1
B34 = Derivative(f, A34)
C34(x) = (B34(a) * (x - a)^(A34) / A34!)
A35: A34 + 1
B35 = Derivative(f, A35)
C35(x) = (B35(a) * (x - a)^(A35) / A35!)
A36: A35 + 1
B36 = Derivative(f, A36)
C36(x) = (B36(a) * (x - a)^(A36) / A36!)
A37: A36 + 1
B37 = Derivative(f, A37)
C37(x) = (B37(a) * (x - a)^(A37) / A37!)
A38: A37 + 1
B38 = Derivative(f, A38)
C38(x) = (B38(a) * (x - a)^(A38) / A38!)
A39: A38 + 1
B39 = Derivative(f, A39)
C39(x) = (B39(a) * (x - a)^(A39) / A39!)
A40: A39 + 1
B40 = Derivative(f, A40)
C40(x) = (B40(a) * (x - a)^(A40) / A40!)
A41: A40 + 1
B41 = Derivative(f, A41)
C41(x) = (B41(a) * (x - a)^(A41) / A41!)
A42: A41 + 1
B42 = Derivative(f, A42)
C42(x) = (B42(a) * (x - a)^(A42) / A42!)
A43: A42 + 1
B43 = Derivative(f, A43)
C43(x) = (B43(a) * (x - a)^(A43) / A43!)
A44: A43 + 1
B44 = Derivative(f, A44)
C44(x) = (B44(a) * (x - a)^(A44) / A44!)
A45: A44 + 1
B45 = Derivative(f, A45)
C45(x) = (B45(a) * (x - a)^(A45) / A45!)
A46: A45 + 1
B46 = Derivative(f, A46)
C46(x) = (B46(a) * (x - a)^(A46) / A46!)
A47: A46 + 1
B47 = Derivative(f, A47)
C47(x) = (B47(a) * (x - a)^(A47) / A47!)
A48: A47 + 1
B48 = Derivative(f, A48)
C48(x) = (B48(a) * (x - a)^(A48) / A48!)
A49: A48 + 1
B49 = Derivative(f, A49)
C49(x) = (B49(a) * (x - a)^(A49) / A49!)
A50: A49 + 1
B50 = Derivative(f, A50)
C50(x) = (B50(a) * (x - a)^(A50) / A50!)
A51: A50 + 1
B51 = Derivative(f, A51)
C51(x) = (B51(a) * (x - a)^(A51) / A51!)
A52: A51 + 1
B52 = Derivative(f, A52)
C52(x) = (B52(a) * (x - a)^(A52) / A52!)
A53: A52 + 1
B53 = Derivative(f, A53)
C53(x) = (B53(a) * (x - a)^(A53) / A53!)
A54: A53 + 1
B54 = Derivative(f, A54)
C54(x) = (B54(a) * (x - a)^(A54) / A54!)
A55: A54 + 1
B55 = Derivative(f, A55)
C55(x) = (B55(a) * (x - a)^(A55) / A55!)
A56: A55 + 1
B56 = Derivative(f, A56)
C56(x) = (B56(a) * (x - a)^(A56) / A56!)
A57: A56 + 1
B57 = Derivative(f, A57)
C57(x) = (B57(a) * (x - a)^(A57) / A57!)
A58: A57 + 1
B58 = Derivative(f, A58)
C58(x) = (B58(a) * (x - a)^(A58) / A58!)
A59: A58 + 1
B59 = Derivative(f, A59)
C59(x) = (B59(a) * (x - a)^(A59) / A59!)
A60: A59 + 1
B60 = Derivative(f, A60)
C60(x) = (B60(a) * (x - a)^(A60) / A60!)
A61: A60 + 1
B61 = Derivative(f, A61)
C61(x) = (B61(a) * (x - a)^(A61) / A61!)
A62: A61 + 1
B62 = Derivative(f, A62)
C62(x) = (B62(a) * (x - a)^(A62) / A62!)
A63: A62 + 1
B63 = Derivative(f, A63)
C63(x) = (B63(a) * (x - a)^(A63) / A63!)
A64: A63 + 1
B64 = Derivative(f, A64)
C64(x) = (B64(a) * (x - a)^(A64) / A64!)
A65: A64 + 1
B65 = Derivative(f, A65)
C65(x) = (B65(a) * (x - a)^(A65) / A65!)
A66: A65 + 1
B66 = Derivative(f, A66)
C66(x) = (B66(a) * (x - a)^(A66) / A66!)
A67: A66 + 1
B67 = Derivative(f, A67)
C67(x) = (B67(a) * (x - a)^(A67) / A67!)
A68: A67 + 1
B68 = Derivative(f, A68)
C68(x) = (B68(a) * (x - a)^(A68) / A68!)
A69: A68 + 1
B69 = Derivative(f, A69)
C69(x) = (B69(a) * (x - a)^(A69) / A69!)
A70: A69 + 1
B70 = Derivative(f, A70)
C70(x) = (B70(a) * (x - a)^(A70) / A70!)
A71: A70 + 1
B71 = Derivative(f, A71)
C71(x) = (B71(a) * (x - a)^(A71) / A71!)
A72: A71 + 1
B72 = Derivative(f, A72)
C72(x) = (B72(a) * (x - a)^(A72) / A72!)
A73: A72 + 1
B73 = Derivative(f, A73)
C73(x) = (B73(a) * (x - a)^(A73) / A73!)
A74: A73 + 1
B74 = Derivative(f, A74)
C74(x) = (B74(a) * (x - a)^(A74) / A74!)
A75: A74 + 1
B75 = Derivative(f, A75)
C75(x) = (B75(a) * (x - a)^(A75) / A75!)
A76: A75 + 1
B76 = Derivative(f, A76)
C76(x) = (B76(a) * (x - a)^(A76) / A76!)
A77: A76 + 1
B77 = Derivative(f, A77)
C77(x) = (B77(a) * (x - a)^(A77) / A77!)
A78: A77 + 1
B78 = Derivative(f, A78)
C78(x) = (B78(a) * (x - a)^(A78) / A78!)
A79: A78 + 1
B79 = Derivative(f, A79)
C79(x) = (B79(a) * (x - a)^(A79) / A79!)
A80: A79 + 1
B80 = Derivative(f, A80)
C80(x) = (B80(a) * (x - a)^(A80) / A80!)
A81: A80 + 1
B81 = Derivative(f, A81)
C81(x) = (B81(a) * (x - a)^(A81) / A81!)
A82: A81 + 1
B82 = Derivative(f, A82)
C82(x) = (B82(a) * (x - a)^(A82) / A82!)
A83: A82 + 1
B83 = Derivative(f, A83)
C83(x) = (B83(a) * (x - a)^(A83) / A83!)
A84: A83 + 1
B84 = Derivative(f, A84)
C84(x) = (B84(a) * (x - a)^(A84) / A84!)
A85: A84 + 1
B85 = Derivative(f, A85)
C85(x) = (B85(a) * (x - a)^(A85) / A85!)
A86: A85 + 1
B86 = Derivative(f, A86)
C86(x) = (B86(a) * (x - a)^(A86) / A86!)
A87: A86 + 1
B87 = Derivative(f, A87)
C87(x) = (B87(a) * (x - a)^(A87) / A87!)
A88: A87 + 1
B88 = Derivative(f, A88)
C88(x) = (B88(a) * (x - a)^(A88) / A88!)
A89: A88 + 1
B89 = Derivative(f, A89)
C89(x) = (B89(a) * (x - a)^(A89) / A89!)
A90: A89 + 1
B90 = Derivative(f, A90)
C90(x) = (B90(a) * (x - a)^(A90) / A90!)
A91: A90 + 1
B91 = Derivative(f, A91)
C91(x) = (B91(a) * (x - a)^(A91) / A91!)
A92: A91 + 1
B92 = Derivative(f, A92)
C92(x) = (B92(a) * (x - a)^(A92) / A92!)
A93: A92 + 1
B93 = Derivative(f, A93)
C93(x) = (B93(a) * (x - a)^(A93) / A93!)
A94: A93 + 1
B94 = Derivative(f, A94)
C94(x) = (B94(a) * (x - a)^(A94) / A94!)
A95: A94 + 1
B95 = Derivative(f, A95)
C95(x) = (B95(a) * (x - a)^(A95) / A95!)
A96: A95 + 1
B96 = Derivative(f, A96)
C96(x) = (B96(a) * (x - a)^(A96) / A96!)
A97: A96 + 1
B97 = Derivative(f, A97)
C97(x) = (B97(a) * (x - a)^(A97) / A97!)
A98: A97 + 1
B98 = Derivative(f, A98)
C98(x) = (B98(a) * (x - a)^(A98) / A98!)
A99: A98 + 1
B99 = Derivative(f, A99)
C99(x) = (B99(a) * (x - a)^(A99) / A99!)
A100: A99 + 1
B100 = Derivative(f, A100)
C100(x) = (B100(a) * (x - a)^(A100) / A100!)
A101: A100 + 1
B101 = Derivative(f, A101)
C101(x) = (B101(a) * (x - a)^(A101) / A101!)
P = TaylorSeries(f, a, n)
E(x) = abs(P(x) - f(x))
text2_{2}: "P_n(x)=" + (LaTeX[P]) + ""
text5: "Reste (erreur) en x_0 d'ordre n: R_n(x)=" + (E(x_0)) + ""