1、1、 (1) 0 . (2) (3) (4). .(5) 26/3 2、 (6) The right proposition in the following propositions is _A_.A. Ifexists anddoes not exist thendoes not exist.B. If,do both not exist thendoes not exist. C. Ifexists anddoes not exist thendoes not exist. D. Ifexists anddoes not exist thendoes not exist.(7) The

2、right proposition in the following propositions is _B_.A. Ifthenexists. B. If thendoes not exist. C. Ifdoes not exist then.D. Ifdoes not exist then the curedoes not have tangent at.(8) The right statement in the following statements is _D_. A. B. C. D. (9) For continuous function, the erroneous expr

3、ession in the following expressions is _D_.A. B. C. D. (10) The right proposition in the following propositions is _B_.A. Ifis discontinuous onthenis unbounded on.B. Ifis unbounded onthenis discontinuous on. C. Ifis bounded onthenis continuous on.D. Ifhas absolute extreme values onthenis continuous

4、on.3、Evaluate （考點(diǎn)課本4.4節(jié)洛比達(dá)法則，每年都會(huì)有一道求極限的解答題，大多數(shù)都是用洛比達(dá)法則去求解，所以大家要注意4.4節(jié)的內(nèi)容。注意洛比達(dá)法則的適用范圍。）4Find andif. （考察微積分基本定理與微分，書上5.3節(jié)）5、 Find= （湊微分求不定積分，積分是微積分的重點(diǎn)及難點(diǎn)，大家一定要掌握透徹。）6、 Given that. (1) Find the intervals on whichis increasing or decreasing. WhenTherefore, the increasing interval is, the decreasing in

5、terval is (2) Find the local maximum and minimum values of The function is increasing in interval, decreasing in interval, therefore, the function exist the local minimum value, it is (3)Find the intervals of concavity and the inflection points.Therefore, the concave upward interval are, the concave

6、 downward interval are, and the inflection points are ,(4) Find the asymptote lines of the cureTherefore, the line is a horizontal asymptote（考點(diǎn)：4.3節(jié)，4.5、4.6節(jié)。近幾年經(jīng)常會(huì)考一道作圖題。這種題目應(yīng)該在注意的點(diǎn)主要包括函數(shù)的定義域，對稱性，增減區(qū)間，極值點(diǎn)，凹凸性，拐點(diǎn)，以及漸近線等。大家參照課本的4.5節(jié)進(jìn)行作圖）7、Let R be the region bounded by the curve , and the line and.(a

7、)Evaluate the area of the region R. R=(b)Find the volume of the solid generated by revolving the R about the y-axis. V=（考點(diǎn)：求面積以及體積，課本6.1、6.2節(jié)。這類題目是常考題，較簡單。望同學(xué)一定要做相應(yīng)的題目加以鞏固。）8、 Determine the production level that will maximize the profit for a company with cost and demand functionsand.Solution Let si

8、nce x>0, then x=400When x=400 Therefore, when the production level is 400 that will maximize the profit 35350 （考點(diǎn)：經(jīng)濟(jì)函數(shù)，課本4.8節(jié)。此題型為常考題，屬于送分題，大家可以做相應(yīng)的4.8節(jié)的練習(xí)加以鞏固） 9、State the second derivative test theorem testing maximum and prove it.Suppose is continuous near c If and , then has a local maximum a

9、t c .Proof: Because near c and so is concave downward near c. This means that the graph of lies below its horizontal tangent at c and so has a local maximum at c. 10、Show that the equationhas at most one root in the interval. Suppose the equation has two rootin the interval.Let then there exist Using the Rolles Theorem we can know that there exist one number c can satisfy But,