101年 - 101 國立臺灣師範大學_學士班轉學生招生考試試題_資訊工程學系二年級：微積分#122187

科目：研究所、轉學考(插大)-微積分 | 年份：101年 | 選擇題數：0 | 申論題數：15

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (15)

(a) (5 points) Express the area of the rectangular portion of the field as a function of x alone.

(b) (5 points) What values of x and r give the rectangular portion the largest possible area?

(a) (4 points) Find lim_x→∞ (x + e^x)^2/x.

(b) (4 points) Evaluate lim_h→0.

3. (8 points) Find the area under the curve y = (lnx)/x² from x = 1 to x = ∞.

4. (8 points) Evaluate the integral.

(a) (8 points) xy' - y = 2x lnx.

(b) (8 points) (x+1)- 2(x² + x)y = , x>−1, y(0) = 5.

(a) (8 points) Let f(x) = x³ – 2. Find the value of df⁻¹/dx at x = 6 = f(2).

(b) (8 points) Find if 2x³ - 3y² = 8.

7. (8 points) Find the length of the parameterized curve x = t³, y = , 0 ≤ t ≤.

8. (8 points) Find the derivative of function g(y), where g(y) =sin(t²)dt.

9. (8 points) The line that is normal to the curve x² + 2xy - 3y² = 0 at (1,1) intersects the curve at what other point?

(a) (5 points) Find the linearization (Taylor polynomial of order 1) at x = 0.

(b) (5 points) Find the quadratic approximation of f at x = 0.