Find the domain of the ve F(t)=(√/t-2₁ e¹ +8 t O (-3, ∞) ○ (0, ∞) O (-3,0) U (0, ∞) O (2, ∞0) O None of these

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Problem Statement:**

Find the domain of the vector function:

\[ \vec{r}(t) = \left\langle \sqrt[3]{t-2}, \frac{e^t + 8}{t}, \ln(t + 3) \right\rangle \]

**Options:**

- \(\circ\) \((-3, \infty)\)
- \(\circ\) \((0, \infty)\)
- \(\circ\) \((-3, 0) \cup (0, \infty)\)
- \(\circ\) \((2, \infty)\)
- \(\circ\) None of these
Transcribed Image Text:**Problem Statement:** Find the domain of the vector function: \[ \vec{r}(t) = \left\langle \sqrt[3]{t-2}, \frac{e^t + 8}{t}, \ln(t + 3) \right\rangle \] **Options:** - \(\circ\) \((-3, \infty)\) - \(\circ\) \((0, \infty)\) - \(\circ\) \((-3, 0) \cup (0, \infty)\) - \(\circ\) \((2, \infty)\) - \(\circ\) None of these
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