ADVANCED MATHEMATICS 内蒙古工业大学托马斯微积分期末试卷

1、 | HYPERLINK / 百度首页 HYPERLINK /v2/?login 登录 HYPERLINK /cashier/browse/vipcashier?dqStatCode=topnav_joinvip&cashier_code=topnav_joinvip VIP意见反馈 HYPERLINK /apps?fr=1011 下载客户端4/13/2019ADVANCED MATHEMATICS 内蒙古工业大学托马斯微积分期末试卷- 百度文库 HYPERLINK /?fr=nav 首页 HYPERLINK javascript:void(0); 分类 HYPERLINK javascrip

2、t:void(0); 精品内容 HYPERLINK /wenkuverify?from=1 申请认证 HYPERLINK javascript:void(0); 机构合作 HYPERLINK javascript:void(0); 频道专区 HYPERLINK /xtopic/wkback 百度智慧课堂 HYPERLINK /user/browse/vip/ 百度教育VIPInner Mongolia University of Technology20092010 academic year/the second term HYPERLINK /?fr=crumbs 百度文库 HYPERLI

3、NK /?fr=crumbs HYPERLINK /edu/index 教育专区 HYPERLINK /edu/index HYPERLINK /list/10 高等教育 HYPERLINK /list/10 HYPERLINK /list/108 理学ADVANCED MATHEMATICSQUARTER(TEST)TEST PAPER(A)(COURSE CODE：090312027)EXAMINER：Zhi-Min-HongTEST TIME：2010.7.13REMARK：.This test paper is used by 2009 science and technologyEn

4、glish.The sum total is six pages. Perfect scores is 100 points.Test time is two hours.CLASS：SERIAL 一NUMBERNAME：NUMBER：二三四五六 PERFECTSCORESMARKSCORE EXAMINER一、Fill in blanks.(3 points each problem)tan x1.lim=x 3x12 x sin,x 0 x = 02. Ifis differentiable at, thenx = 0f ( x) =x0,equation of the tangent l

5、ine to the curve( ) at pointy = f xADVANCEDMATHEMATICSTestPaperTotalsixpages1/view/e32c0c39580216fc700afdb4.html1/7 4/13/2019ADVANCED MATHEMATICS 内蒙古工业大学托马斯微积分期末试卷- 百度文库is.x = 013. Let, thenf (0) =.f (x) = x34. Assume thatis a critical point of function, thenf (x)x = x0.f (x ) =0SCORE EXAMINER二、Disc

6、ussing.(8 points)Find the values of and such thatabax + b,x -1x -1f (x) = ax + x + 2b,3is differentiable at the point x = -1.ADVANCEDMATHEMATICSTestPaperTotalsixpages2/view/e32c0c39580216fc700afdb4.html2/7 4/13/2019ADVANCED MATHEMATICS 内蒙古工业大学托马斯微积分期末试卷- 百度文库SCORE EXAMINER三、Compute the following lim

7、its.(6 pointseach problem)2 - + sintt1.lim+ cost -tt1 - cosx2.limx 0 e - x - 1x33. lim (1 + ) .xx x26 -5+ 11 + 6xx4. lim.-x 0 xADVANCEDMATHEMATICSTestPaperTotalsixpages3/view/e32c0c39580216fc700afdb4.html3/7 4/13/2019ADVANCED MATHEMATICS 内蒙古工业大学托马斯微积分期末试卷- 百度文库SCORE EXAMINER四、Find the derivatives of

8、 the followingfunctions.(6pointseach problem)x1dy1. If, evaluatedt + ln( 3 + e).y = 2t + 1dxsec x2 x = sec t - 1dydx2. Let,find the derivative., t = -y = tan t43. Letx,find the derivative.y = (sin x)yADVANCEDMATHEMATICSTestPaperTotalsixpages4/view/e32c0c39580216fc700afdb4.html4/7 4/13/2019ADVANCED M

9、ATHEMATICS 内蒙古工业大学托马斯微积分期末试卷- 百度文库五、Evaluate the following indefinite andSCORE EXAMINERdefinite integrals.(6 points each problem)cos(1 - ln x)1.dxxe2.3. x ln xdx1cos x3.dxx sinx32 / 414.dx .29 - 4 x0ADVANCEDMATHEMATICSTestPaperTotalsixpages5/view/e32c0c39580216fc700afdb4.html5/7 4/13/2019ADVANCED MATHEMATICS 内蒙古工业大学托马斯微积分期末试卷- 百度文库六、Let,determine the regionsy = x 3 - xSCORE EXAMINERof increase and decrease, the regions ofconcave up and concave down, extreme valuepoints and inflection points.(14 points)ADVANCEDMATHEMATICS