1. Evaluate the limit , if it exist. (1) lim 1－√1－x*2 / x x→0 (2) lim x*3 / tan*3 2x x→0 2. Draw the graph of f(x)= 4－│x－2│ (1) Is f continuous at x=2 ? (Explain it by definition) (2) Is f differentiable at x=2 ? (Explain it by definition) 3. Find y' , if y = sin ( tan √ sinx ) 4. Show that x*101 + x*51 + x － 2 ＝ 0 has exactly one real root . 出处4-1 NO.69 5. Show that the curves 2x*2 + y*2 = 3 and x = y*2 are orthogonal. 出处3-7 NO.41 6. Let g(x) = f(x*2) , where f is twice differentiable for all x , f'(x) > 0 for all x ≠ 0 , and f is concave downward on (－∞ , 0 ) and concave upward on ( 0 , ∞ ) . (1) At what numbers does g have an extreme value ? (2) Discuss the concavity of g . 出处4-REVIEW NO.37 7. State the Mean Value Theorem and use it to prove that √1 + x < 1 + 1/2 x if x > 0 . 出处4-2 NO.27 8. Sketch the graph of y = x / x*2 － 9 出处4-5 NO.12 因为跟徐老的国文奋斗的有点久 所以就无聊来看看微积分 前面三题我懒得找了很简单後面五题都是从後面习题出来的 我有找到出处 至於是不是老师勾的 我就不知道了我又没去上过几次课.... 几乎都是第4章的要临时抱佛脚的快把第四章看一下吧~ 祝大家应考顺利阿 有看有保佑阿 我要继续跟徐老师奋斗了 希望早上七点前写的完.... --

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