Adiciona questão 05 da prova de 2018

src/lib/autores/autores.json

@@ -9,5 +9,11 @@
         "nome": "Matheus Alves dos Santos",
         "email": "[email protected]",
         "github": "alvesmatheus"
+    },
+
+    "3": {
+        "nome": "Valter Vinícius Marinho de Lucena",
+        "email": "[email protected]",
+        "github": "valterlucena"
     }
 }

src/lib/provas/2018/5.json

@@ -0,0 +1,18 @@
+{
+    "ano": "2018",
+    "questao": "5",
+    "area": "Matemática",
+    "enunciado": "Calcule o limite de $\lim_{x \to \infty }(\sqrt{x^4+x^2} + \sqrt{x^2+5x} - x² - x)$:", 
+    "img_url": [],
+    "alternativas": {
+        "A": "1", 
+        "B": "5", 
+        "C": "∞", 
+        "D": "0", 
+        "E": "3"
+    },
+    "resposta": "E",
+    "autor": ["3"],
+    "temas": ["Limites"],
+    "justificativa": "$\lim_{x \to \infty }(\sqrt{x^4+x^2} + \sqrt{x^2+5x} - x^2 - x) \newline= \lim_{x \to \infty }(\sqrt{x^4+x^2} - x^2) + \lim_{x \to \infty }(\sqrt{x^2+5x} - x) \newline=\lim_{x \to \infty }[(\sqrt{x^4+x^2} - x^2)\frac{(\sqrt{x^4+x^2} + x^2)}{(\sqrt{x^4+x^2} + x^2)}] + \lim_{x \to \infty }[(\sqrt{x^2+5x} - x)\frac{(\sqrt{x^2+5x} + x)}{(\sqrt{x^2+5x} + x)}] \newline= \lim_{x \to \infty }(\frac{x^2}{\sqrt{x^4+x^2} + x^2}) + \lim_{x \to \infty }(\frac{5x}{\sqrt{x^2+5x} + x}) = \lim_{x \to \infty }[\frac{x^2}{x^2(\frac{\sqrt{x^4+x^2}}{x^2} + 1)}] + \lim_{x \to \infty }[\frac{5x}{x(\frac{\sqrt{x^2+5x}}{x} + 1)}]\newline= \lim_{x \to \infty }(\frac{1}{\frac{\sqrt{x^4+x^2}}{x^2} + 1}) + \lim_{x \to \infty }(\frac{5}{\frac{\sqrt{x^2+5x}}{x} + 1})\newline=\lim_{x \to \infty }[\frac{1}{\frac{\sqrt{x^4(1+\frac{1}{x^2})}}{x^2} + 1}] + \lim_{x \to \infty }[\frac{5}{\frac{\sqrt{x^2(1+\frac{5}{x})}}{x} + 1}]\newline=\lim_{x \to \infty }[\frac{1}{\frac{x^2\sqrt{1+\frac{1}{x^2}}}{x^2} + 1}] + \lim_{x \to \infty }[\frac{5}{\frac{x\sqrt{1+\frac{5}{x}}}{x} + 1}]\newline=\lim_{x \to \infty }(\frac{1}{\sqrt{1+\frac{1}{x^2}} + 1}) + \lim_{x \to \infty }(\frac{5}{\sqrt{1+\frac{5}{x}} + 1})\newline=\frac{1}{\sqrt{1+0} + 1} + \frac{5}{\sqrt{1+0} + 1}\newline=\frac{1}{\sqrt{1} + 1} + \frac{5}{\sqrt{1} + 1}\newline=\frac{1}{2} + \frac{5}{2} = 3$"
+}