vault backup: 2026-02-21 22:40:01

Estudos/Cálculo/.vscode/settings.json

@@ -0,0 +1,4 @@
+{
+    "python-envs.defaultEnvManager": "ms-python.python:system",
+    "python-envs.pythonProjects": []
+}

Estudos/Cálculo/3_graph.py

@@ -0,0 +1,36 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+# f(x) = sqrt(2(x^2 - 8)) + x, for x < -4
+# f(x) = 2^(x+4), for x >= -4
+
+x1 = np.linspace(-12, -4, 500, endpoint=False)
+y1 = np.sqrt(2 * (x1**2 - 8)) + x1
+
+x2 = np.linspace(-4, 4, 500)
+y2 = 2 ** (x2 + 4)
+
+plt.figure(figsize=(8, 5))
+plt.plot(x1, y1, label=r"$f(x)=\sqrt{2(x^2-8)}+x$, $x<-4$", color="tab:blue")
+plt.plot(x2, y2, label=r"$f(x)=2^{x+4}$, $x\\ge -4$", color="tab:orange")
+
+# Open circle at x = -4 for first branch
+y_left_limit = np.sqrt(2 * ((-4) ** 2 - 8)) - 4
+plt.scatter(-4, y_left_limit, facecolors="white", edgecolors="tab:blue", s=80, zorder=5)
+
+# Closed circle at x = -4 for second branch
+y_at_minus4 = 2 ** (0)
+plt.scatter(-4, y_at_minus4, color="tab:orange", s=80, zorder=5)
+
+plt.axhline(0, color="black", linewidth=0.8)
+plt.axvline(0, color="black", linewidth=0.8)
+plt.grid(True, linestyle="--", alpha=0.5)
+plt.xlim(-12, 4)
+plt.ylim(-2, max(y2) * 1.1)
+plt.title("Graph of the piecewise function f(x)")
+plt.xlabel("x")
+plt.ylabel("f(x)")
+plt.legend()
+plt.tight_layout()
+plt.show()

Estudos/Cálculo/Avaliação.md

@@ -24,6 +24,5 @@ $$
 y'=\small \dfrac{7}{2}. x^2\sqrt{x}+5x^4
 $$
 # 3. 
-$$
-\s
-$$
+$f(x) = \sqrt{2(x^2 - 8)}+x$ se $x<-4$
+$f(x) = 2^{x+4}$ se $x\ge-4$