# Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 611: 19

$$1$$

#### Work Step by Step

Since speed is given by \begin{align*} \frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\ &=\sqrt{ 4t^2+e^{2t} } \end{align*} Then \begin{align*} \frac{d s}{d t}\bigg|_{t=0} &=\sqrt{ 4t^2+e^{2t} } \\ &=1 \end{align*}

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