import{c as u}from"./courbes-HH5ni-HU.js";import{r as g}from"./reperes-MjYMQS1W.js";import{E as C,ai as _,h as m,r as M,o as q,l as Q}from"./index-hc8lvKav.js";const L="Lecture graphique de limites",E="01/02/2022",A="09/02/2022";function F(){C.call(this),this.nbQuestions=3,this.sup=!1,this.sup2=!1,this.nouvelleVersion=function(){this.listeQuestions=[],this.listeCorrections=[],this.autoCorrection=[];for(let a=0,h,s,f=0;a<this.nbQuestions&&f<50;){const n=["f","g","h","p","q","r","s"][a%7];h=`Déterminer graphiquement les ${this.sup2?"limites et asymtpotes":"limites"} de la fonction $${n}$ dont la courbe représentative est tracée ci-dessous.<br>`,s="";let e=[-5,-4,-3,-2,-1,0,1,2,3,4,5];e=_(e),e=e.slice(0,m([a!==0?0:2,1,1,2,2,3])),e=e.sort((t,i)=>t-i);const y=e.slice(),r=[],l=g(),c=M(-5,5),x=M(-5,5,[c]);if(e.length!==0){{const t=c,i=m([-1,1]),o=$=>t+i*1/($-e[0]);r.push(u(o,{color:"red",repere:l,xMin:-10,xMax:e[0]-.5,yMin:-10,yMax:10,step:.1})),r.push(u(o,{color:"red",repere:l,xMin:e[0]-.5,xMax:e[0]-.001,yMin:-10,yMax:10,step:.001})),y.push(t,i),s+=`$\\displaystyle\\lim_{x \\to -\\infty} ${n}(x) = ${t}$<br>`,s+=`$\\displaystyle\\lim_{${d(e[0],"-")}} ${n}(x) = ${i<0?"+\\infty":"-\\infty"}$<br>`}for(let t=0;t<e.length-1;t++){const i=m([-1,1]),o=m([-1,1]),$=M(-3,3),p=b=>i*1/(b-e[t])+$+o*1/(b-e[t+1]);r.push(u(p,{color:"red",repere:l,xMin:e[t]+.001,xMax:e[t]+.5,yMin:-10,yMax:10,step:.001})),r.push(u(p,{color:"red",repere:l,xMin:e[t]+.5,xMax:e[t+1]-.5,yMin:-10,yMax:10,step:.1})),r.push(u(p,{color:"red",repere:l,xMin:e[t+1]-.5,xMax:e[t+1]-.001,yMin:-10,yMax:10,step:.001})),y.push(i,o),s+=`$\\displaystyle\\lim_{${d(e[t],"+")}} ${n}(x) = ${i>0?"+\\infty":"-\\infty"}$<br>`,s+=`$\\displaystyle\\lim_{${d(e[t+1],"-")}} ${n}(x) = ${o<0?"+\\infty":"-\\infty"}$<br>`}{const t=m([-1,1]),i=x,o=$=>t*1/($-e[e.length-1])+i;r.push(u(o,{color:"red",repere:l,xMin:e[e.length-1]+.001,xMax:e[e.length-1]+.5,yMin:-10,yMax:10,step:.001})),r.push(u(o,{color:"red",repere:l,xMin:e[e.length-1]+.5,xMax:10,yMin:-10,yMax:10,step:.1})),y.push(t,i),s+=`$\\displaystyle\\lim_{${d(e[e.length-1],"+")}} ${n}(x) = ${t>0?"+\\infty":"-\\infty"}$<br>`,s+=`$\\displaystyle\\lim_{x \\to +\\infty} ${n}(x) = ${i}$<br>`}}else{const t=(c-x)/4e3,i=-3/40*(c-x),o=(c+x)/2,$=p=>t*p*p*p+i*p+o;r.push(u($,{color:"red",repere:l,xMin:-10,xMax:10,yMin:-10,yMax:10,step:.1})),y.push("∅",c,x),s+=`$\\displaystyle\\lim_{x \\to -\\infty} ${n}(x) = ${c}$<br>`,s+=`$\\displaystyle\\lim_{x \\to +\\infty} ${n}(x) = ${x}$<br>`}if(this.sup2)switch(s+=`La courbe admet les asymptotes horizontales d'équations $y=${c}$ et $y=${x}$.<br>`,e.length){case 0:break;case 1:s+=`La courbe admet une asymptote verticale d'équation $x=${e[0]}$.<br>`;break;default:s+=`La courbe admet les asymptotes verticales d'équations ${e.map((t,i)=>(i===e.length-1?" et ":", ")+"$x="+t+"$ ").join("").substring(2)}.<br>`}h+=q({xmin:-10,ymin:-10,xmax:10,ymax:10,scale:.5},l,...r),this.questionJamaisPosee(a,y)&&(this.listeQuestions.push(h),this.listeCorrections.push(s),a++),f++}Q(this)},this.besoinFormulaireCaseACocher=["Notation x>2 au lieu de 2+"];const d=(a,h)=>{let s=this.sup?"\\substack{":"";return s+=`x \\to ${a}`,s+=this.sup?`\\\\x ${h==="+"?">":"<"} ${a}}`:`^${h}`,s};this.besoinFormulaire2CaseACocher=["Question sur les asymptotes"]}export{A as dateDeModifImportante,E as dateDePublication,F as default,L as titre};
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