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Using differential methods, find the formula with slope $\frac{dy}{dx} = 2x$.
What is $\frac{dx}{dy}$ given $\frac{x^2}{a^2} – \frac{y^2}{b^2} = 1$?
Sketch the slope field associated with your answer from the previous question ($\frac{dy}{dx} = \frac{b^2x}{a^2y}$) when $ a = b = 1$.
What is the equation of the graph $\frac{dy}{dx} = y^2x^2$?
Given the parametric definition of a hyperbola $x = a*\sec(t), y = b*\tan(t)$, graph this for when $ a = b = 1$ over $0 \leq t \leq 2\pi$.
Use the parametric definition of the hyperbola and your value for $\frac{dx}{dy} = \frac{b^2x}{a^2y}$ from quiz question 1 to find $\lim_{t \to \frac{\pi}{2}} \frac{dy}{dx}$.