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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.

其他申論題

6.(5%)Prove using the ε,δ definition of a limit.

7. (5%)Find if ycosx = 1 + sin(xy).

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._________.

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

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 .Then f"(x)=__(8)__.

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

I. (50 points) Fill in the following blanks.1. Find the Taylor series of In(1+x)centered at x=0, __(1)__.

2. Suppose f(x, y)=4e-2(x+y),0＜x,y＜∞.Weknow that w=x+y.Then f(w)=_________.

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

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