MATH 3A

Final - Practice 1 | General | Grigoryan

If the function is given implicitly by $xe^y - 3y \sin x = 1$, find $y'$ by implicit differentiation.

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Sketch the graph of the function $f(x) = \frac{5x}{x^3 - x}$ by first finding:
(a) The domain and asymptotes.
(b) Intervals of monotonicity and concavity.
(c) Local extrema and inflection points.

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3. A boat leaves the dock at 2 pm. and travels due south at a speed of 20 km/h. Another boat has been heading due east at 10 km/h and reaches the dock at 3 pm. At what time were the two boats closest to each other?

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4. Find the limits.

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5. Find the equation of the tangent line to the curve $e^x$ that passes through the origin.

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