微积分英文ppt课件

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Review,Review,1,Example,一、,is continuous at,Limits,a.,Example一、is continuou,2,二,二,3,b.,Example,b.Example,4,c.,Example,c.Example,5,d.,Example,d.Example,6,e.,Example,e.Example,7,Example,Example,8,f.,Example,f.Example,9,g.,Example,g.Example,10,j.,Example,k.,Example,j.Examplek.Example,11,无穷小,有界,机动 目录 上页 下页 返回 结束,Example,无穷小有界机动 目录 上页 下页 返回,12,exists?If so,find the value of and the value of,the limit.,Is there a number such that,Solution,Because,Example,exists?If so,find the value,13,If we know that the limit,does not exist,it follows that the value of must be 0,namely,so,If we,14,True or false,1.,2.,3.,True or false1.2.3.,15,4.If,5.,then does not exist。,If,then does not exist。,True or false,and,and,4.If5.then,16,6.If exists,7.,Then the limit must be 。,If,then,Example,True or false,and,6.If,17,8.If exists,9.,then exists。,If,then there exists a number between 1 and 3 such that,True or false,8.If,18,10.,If,and,then,True or false,exists,10.IfandthenTrue or falseexist,19,三、Choose the best answer for each of the,Following,1.If,then,k,=_.,2.If,then,k,=_.,三、Choose the best answer for e,20,四、,Fill in the blanks:,四、Fill in the blanks:,21,Example If,is continuous at,x,=0,then,a,=,b,=,.,机动 目录 上页 下页 返回 结束,Example Ifis continuous at x=,22,Find,a,and,b.,机动 目录 上页 下页 返回 结束,Example If,has an,infinite discontinuity,at,and has a removable discontinuity at,Find a and b.机动 目录 上页,23,Solution,So,does not exist.,机动 目录 上页 下页 返回 结束,Because has an,infinite discontinuity,at ,so,Because,has a removable discontinuity at,SolutionSo,24,Example,Find,a,b,such that,机动 目录 上页 下页 返回 结束,Solution,Since,thus,Example Find a,b,such tha,25,机动 目录 上页 下页 返回 结束,therefore,机动 目录 上页 下页 返回 结束 th,26,机动 目录 上页 下页 返回 结束,Example,Find the points of discontinuity and identify its,type,where,机动 目录 上页 下页 返回 结束 Ex,27,x,=1.,x,=1.,x,=0.,机动 目录 上页 下页 返回 结束,has a removable discontinuity at,has a jump discontinuity at,has an infinite discontinuity at,x=1.x=1.x=0.机动 目录,28,Example,Find,Solution,机动 目录 上页 下页 返回 结束,Example FindSolution机动 目录,29,机动 目录 上页 下页 返回 结束,Let,Then,Example,Find,Using the,Squeeze Theorem,we get,机动 目录 上页 下页 返回 结束 Le,30,六、,Example,Show that there is a root of the equation,between 0 and 1.,六、ExampleShow that there is a,31,Solution,Let,We have,Thus N=0 is a number between g(0)and g(2).,Since g is continuous on 0,1,so the Intermediate,Value Theorem says there is a number c between,0 and 1 such that g(c)=0.,That is,SolutionLetWe haveThus N=0 is,32,六、,Example,Prove that the equation,has exactly one real root。,六、ExampleProve that the equati,33,1.If,then,=_.,Fill in the blanks:,2.If,then,=_.,1.If,then=_.Fill in the,34,3.If,then,=_.,Fill in the blanks:,4.If,then,=_.,3.If,then=_.Fill in the,35,5.If,then,=_.,6.If,then,=_.,Fill in the blanks:,5.If,then=_.6.Ifthen=_,36,5.If is continuous at and,then,=_.,Fill in the blanks:,5.If is continuous,37,7.If,then,=_.,then,a,=_.,7.If,then=_.,thena=_,38,Derivatives,一、The chain rule,Example,Differentiate the function,Derivatives一、The chain rule Ex,39,Example,Find,1.if,ExampleFind1.if,40,二、Implicit Differentiation,Example,1.Find if,2.Find and if,二、Implicit DifferentiationExam,41,Example,1.Find if,三、Higher Derivatives,2.Find if,Example1.Find if 三、Higher,42,Example,1.Find if,四、,logarithmic differentiation,2.Find if,Example1.Find if 四、logari,43,五、Differential,Find if,Example,五、DifferentialFind if Exam,44,Let,Find the values of a and b that make,differentiable everywhere.,Because f is differentiable everywhere,thus,f is continuous and differentiable at x=0,Example,Solution,Let Find the values of a and b,45,Let,Find the values of a and b that make,differentiable at .,Because f is differentiable at ,thus,f is continuous at x=0.,Example,Solution,Since f is continuous at x=0,Let Find the values of a and b,46,Thus,Since f is differentiable at,Thus,ThusSince f is differentiabl,47,微积分英文ppt课件,48,