97年 - 97 國立政治大學轉學生招生考試_應用數學系：微積分(一)#122386

1. Prove that (f(x)+g(x)) = L₁ + L₂, if = L₁ and g(x) = L2. (10 pts)

① Find all the relative maxima and minima.

② Determine the intervals where the function is decreasing or increasing.

③Determine the concavity.

④Find all the asymptotes.

⑤Sketch the graph.

4. Find the derivative of f(x, y) = xe^y + cos(xy) at the point (2, 0) in the direction of the vector . (10 pts)

①

②.

7. Graph the curve r² = 4cos θ. (10 pts)

①y = , x>2.

②y = z sec^-1z - ＞z>1.

③ y = 2

④ x + sin(y) = xy.