95年 - 95 國立政治大學轉學生招生考試_應用數學系：微積分(一)#122906

1. Use the definition to show thatx² = 4.

2. Prove or disprove that if f(x) is continuous at x = a, then f(x) is differentiable at x = a.

3. If f(x) is continuous on [0, 1], show that there exists c in [0, 1], such that f(c) = c.

5. Graph.

6. Show that the balance of P dollars invested for x years at the annual interest rate r compounded continuously is Pe^(rx) dollars.

7. In the method of Lagrange multipliers, f(x, y) is the objective function, g(x,y) = 0 is the constraint, and (xo, yo) is the only solution. Evaluate.

8. Find the Maclaurin series of and its radius of convergence.

9. When is f(x, y) differentiable at (a, b)?

10. Find if possible.

95年 - 95 國立政治大學轉學生招生考試_應用數學系：微積分(一)#122906

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