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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 10.2.2 .
For each of the following vector-valued functions, state any values of
\(a\) for which
\(\displaystyle\lim_{t\to a}\vr(t)\) will
not exist and find
\(\vr\, '(t)\text{.}\)
(a)
\(\vr(t) = \langle \cos(t), t\sin(t), \ln(t) \rangle\text{.}\)
(b)
\(\vr(t) = \langle t^2 + 3t, e^{-2t}, \displaystyle\frac{t}{t^2 + 1} \rangle\text{.}\)
(c)
\(\vr(t) = \langle \tan(t), \cos(t^2), te^{-t} \rangle\text{.}\)
(d)
\(\vr(t) = \left\langle \sqrt{t^4 + 4}, \frac{2}{t^2+t} , e^{2t} \sin(-2t) \right\rangle\text{.}\)
