Post-Video Questions Preview

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Here are some questions you’ll be asked after you finish watching the videos. Please read through these before watching the videos.

Determine the slope of the line tangent to the curve $x^2 + y^2 = 25$ at the point $(4, 3)$ .

Suppose $x$ and $y$ are related by the equation $\cos (y) = xy$ . Further suppose that $x$ changes by a very small amount, represented by $dx$ . Write an expression for the corresponding change in $y$ .

Suppose $x$ and $y$ represent the measures of covarying quantities and that the covariation of $x$ and $y$ is constrained by the equation $x^2 + 5y^5 = 9$ . At what rate does $y$ change with respect to $x$ when $x = 2$ and $y = 1$ ?