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# Suppose $u$ and $v$ are vector functions that possess limits as $t \to a$ and let $c$ be a constant. Prove the following properties of limits.(a) $\displaystyle \lim_{t \to a} [u(t) + v(t)] = \displaystyle \lim_{t \to a} u(t) + \displaystyle \lim_{t \to a} v(t)$(b) $\displaystyle \lim_{t \to a} cu(t) = c \displaystyle \lim_{t \to a} u(t)$(c) $\displaystyle \lim_{t \to a} [u(t) \cdot v(t)] = \displaystyle \lim_{t \to a} u(t) \cdot \displaystyle \lim_{t \to a} v(t)$(d) $\displaystyle \lim_{t \to a} [u(t) \times v(t)] = \displaystyle \lim_{t \to a} u(t) \times \displaystyle \lim_{t \to a} v(t)$

## a. See work for answerb. $\lim _{x \rightarrow a}[c \cdot f(x)]=c \lim _{x \rightarrow a} f(x)$c. see work for answerd. see work for answer

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