104年 - 104 國立臺北大學_轉學生招生考試試題_經濟學系二年級：微積分#118776

I. (50 points) Fill in the following blanks.

1. Find the tangent line to function y=3x²-5x+2 at x=2. Express your answer in the form y=mx+b with slope m and y-intercept b.___(1)__.

2. Find the derivative of (x² +1)(x²+3x+2),__(2)__ ; and the derivative of ,__(3)__.

3. Let function f(x)=3x⁵-5x³ has domain D₁=[-], then its global maximum is at __(4)__ on D_1. Let function has domain D₂ =[1,10], then its global minimum is at __(5)__ on D₂.

4. Suppose f(x)=x³ and x=(z-1)(z+1).Then=__(6)__. (Please express it in z.)

Suppose=__ (7)__ . (Please express it in z.)

5.Suppose=__(8)__.

6. The value of sin(x²)dx is__(9)__ , and the value ofxin xdx is __(10)__.

II. (50 points) Fill in the following blanks.

1. Find the Taylor series of In(1+x) centered at x=0,__(1)__.

2. Suppose,0＜x,y＜∞.Weknow that w=x+y.Then f(w)=__(2)__.

3. Let f be an integrable function on [a, b] and a ＜d ＜b. Suppose and=__(3)__.

4. The value of is__(4)__.

5. The value of is__(5)__.

104年 - 104 國立臺北大學_轉學生招生考試試題_經濟學系二年級：微積分#118776

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