Q4 Tangent line
10 Points
Let \( C \) be the curve parameterized by \( \mathbf{r}(t)=\left\langle\ln (t+1), t \sin 2 t, 3^{t}\right\rangle \) for \( -1<t<1 \). Find a parameterization for the tangent line to \( C \) at the point \( \langle 0,0,1\rangle \).
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