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研究所、轉學考(插大)-微積分
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104年 - 104 國立臺北大學學士班暨進修學士班轉學生招生考試試題_經濟學系學士班暨進修學士班二年級：微積分#116801
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1.Find the tangent line to function y=3x
2
-5x+2 at x=2 . Express your answer in the form y=mx+b with slope m and y-intercept b._________.
其他申論題
(d)
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5. (20%)Please sketch the curve y = . (You must describe the domain, intercepts, symmetry, asymptotes, interval of increasing or decreasing, local maximum and minimum values, and concavity and points of inflection.)
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6.(5%)Prove using the ε,δ definition of a limit.
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7. (5%)Find if ycosx = 1 + sin(xy).
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2. Find the derivative of(x2+1)(x2+3x+2),__(2)__ ; and the derivative of,__(3)__ .
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3. Let function f(x)=3x5-5x3 has domain , then its global maximum is at __(4)__ on D1. Let function g(x)=3x+5+ has domain D2 =[1,10], then its global minimum is at__(5)__on D2.
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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.) .
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5. Suppose .Then f"(x)=__(8)__.
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6. The value of sin(x2)dx is__(9)__ , and the value ofxIn xdx is__(10)__.
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I. (50 points) Fill in the following blanks.1. Find the Taylor series of In(1+x)centered at x=0, __(1)__.
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