=====Mathematics 250 - Spring 2016===== ==== Homework ==== Evaluate the following limits: 1. $\lim\limits_{x \to 1}F(x)$, where $F(x) = (x^2 - 4, 3x + 4)$. 2. $\lim\limits_{t \to \pi}G(t)$, where $G(t) = (\cos(2t), \sin(2t), 2t, \cos(t))$. 3. $\lim\limits_{x \uparrow 2}F(x)$, where $F(x) = (x, \sqrt{4 - x^2})$. 4. $\lim\limits_{t \to \infty}F(t)$, where $F(t) = \left(t^2e^{-2t}, \frac{t+1}{t-1}\right)$. 5. Let $F(t) = (\cos(t), \sin(t))$. Explain why $\lim\limits_{t \to \infty}\|F(t)\|$ exists, but $\lim\limits_{t \to \infty}F(t)$ does not exist. Answers: - $(-3, 7)$ - $(1, 0, 2\pi, -1)$ - $(2, 0)$ - $(0, 1)$