Video Set Introduction

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Before watching the videos, think about and answer these questions to the best of your ability.

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

$\frac {4}{5}$ $\frac {-4}{5}$ $\frac {3}{4}$ $\frac {-3}{4}$ $\frac {3}{5}$ $\frac {-3}{5}$

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

$\frac {1}{\cos (y)+1}$ $\frac {1}{\cos (x)+1}$ $\frac {\cos (y)}{x}$ $\frac {x}{\cos (y)}$

Suppose $x$ and $y$ represent the measures of covarying quantities and that the covariation of $x$ and $y$ is constrained by the equation $x^2 + 2y^3 = 11$ . At what rate does $y$ change with respect to $x$ when $x = 3$ and $y = 1$ ?

$3$ $1$ $0$ $-1$ $\frac {1}{3}$