{"nodes":[{"title":"D\u00e9rivabilit\u00e9 - 1er L","body":"
\t\t$\\Rightarrow\\ \\lim\\limits_{n\\;\\longrightarrow+\\infty}U_{p}+(n-P)\\times r=\\pm\\infty$
\t\u00a0
\t\u00a0
\t\u00a0
$\\begin{array}{rcl} \\alpha\\overrightarrow{GA}+\\beta\\overrightarrow{GB}+\\gamma\\overrightarrow{GC}+\\delta\\overrightarrow{GD}=\\vec{0} &\\Leftrightarrow & \\alpha\\overrightarrow{GA}+\\beta\\left(\\overrightarrow{GA}+\\overrightarrow{AB}\\right)+\\gamma\\left(\\overrightarrow{GA}+\\overrightarrow{AC}\\right)+\\delta\\left(\\overrightarrow{GA}+\\overrightarrow{AD}\\right)=\\vec{0}\\\\\\\\ &\\Leftrightarrow &(\\alpha+\\beta+\\gamma+\\delta)\\overrightarrow{GA}+\\beta\\overrightarrow{AB}+\\gamma\\overrightarrow{AC}+\\delta\\overrightarrow{AD}=\\overrightarrow{0}\\\\\\\\ &\\Leftrightarrow &(\\alpha+\\beta+\\gamma+\\delta)\\overrightarrow{AG}=\\beta\\overrightarrow{AB}+\\gamma\\overrightarrow{AC}+\\delta\\overrightarrow{AD}\\\\\\\\ &\\Leftrightarrow & \\overrightarrow{AG}=\\dfrac{\\beta}{\\alpha+\\beta+\\gamma+\\delta}\\overrightarrow{AB}+\\dfrac{\\gamma}{\\alpha+\\beta+\\gamma+\\delta}\\overrightarrow{AC}+\\dfrac{\\delta} {\\alpha+\\beta+\\gamma+\\delta}\\overrightarrow{AD}\\quad(2)\\end{array}$
\n\t\u00a0
\tdonc $\\lim\\limits_{x\\rightarrow +\\infty}x^{2}-2x+1=\\lim\\limits_{x\\rightarrow +\\infty}x^{2}=+\\infty$
\t\u00a0
\t
\t
\t
\t
\t\u00a0
\t$\\begin{array}{rcl} \\cos\\dfrac{77\\pi}{4}&=&\\cos\\left(-\\dfrac{3\\pi}{4}\\right)\\\\ \\\\&=&\\cos\\dfrac{3\\pi}{4}\\\\ \\\\&=&\\cos\\left(\\pi-\\dfrac{\\pi}{4}\\right)\\\\ \\\\&=&-\\cos\\dfrac{\\pi}{4}\\\\ \\\\&=&-\\dfrac{\\sqrt{2}}{2}\\end{array}$
Rappel : signes des solutions de $ax^{2}+bx+c=0\\quad(a\\neq 0)$
\n\t
\t
\t\u00a0