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{PARA 0 "" 0 "" {TEXT -1 46 "Soit g la solution de (E) telle que g(x_i)=y_i" }}{PARA 0 "" 0 "" {TEXT -1 13 "On a alors : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "D(g)(x)=f(x,g(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--%\"DG6# %\"gG6#%\"xG-%\"fG6$F*-F(F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Don c : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "D(g)(x[i])=f(x[i],g (x[i]));\nD(g)(x[i])=f(x[i],y[i]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/--%\"DG6#%\"gG6#&%\"xG6#%\"iG-%\"fG6$F*-F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/--%\"DG6#%\"gG6#&%\"xG6#%\"iG-%\"fG6$F*&%\"yGF," }}} {EXCHG {PARA 0 "" 0 "" {TEXT 259 49 "L'\351quation de la tangente de g en x_i est donc : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "y=f( x[i],y[i])*(x-x_i)+y[i];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&*& -%\"fG6$&%\"xG6#%\"iG&F$F,\"\"\",&F+F/%$x_iG!\"\"F/F/F.F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "La solution F approch\351e propos\351e p ar la m\351thode d'Euler admet donc pour expression sur 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