Chapter 2 - Section 2.1 - Rates of Change and Tangents to Curves - Exercises - Page 56: 5

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$R(\theta)=\sqrt{4(\theta)+1} , [0,2]$ $$\frac{\Delta{y}}{\Delta{x}}=\frac{R(\theta_{2})-R(\theta_{1})}{\theta_{2}-\theta_{1}}$$ $R(\theta_{2})=R(2)=\sqrt{4(2)+1}$ $R(2)=\sqrt{9}$ $R(2)=3$ $R(\theta_{1})=R(0)=\sqrt{4(0)+1}$ $R(0)=\sqrt{1}$ $R(0)=1$ $$\frac{\Delta{y}}{\Delta{x}}=\frac{R(2)-R(0)}{\theta_{2}-\theta_{1}}$$ $$\frac{\Delta{y}}{\Delta{x}}=\frac{3-1}{2-0}$$ $$\frac{\Delta{y}}{\Delta{x}}=\frac{2}{2}=1$$