【微积分月考试卷】Calculus Test 1.doc

ZheJiang University Of Science And Technology Civil Engineering 14 Middle TestCalculus I-II Middle Chinese Test (2015.04)Name Id Class Grade Cautions:1While discussing the convergence of series,you have to give the name of the law used to identify it.2This paper contains two chapters:Chap 11-12.If you cant finish this smoothly,read the book.1. (25 points)Solve the following questions,finding their limits or integral them to find the answer.第 4 页 共 4 页2. (8 points)Choosing center for Taylor Series,here are several given functions1find the convergence of Taylor Series when a=0 2if it is convergent,choose a appropriate Taylor Series near the given function of x. near x=1.03 near x=1.0033. (7 points)4. (20 points) 1Find the seriess radius and interval of convergence 2discuss its function of sum.There is a constant a,and,please show that f(x) converges,and find it is convergent conditionally or absolutely.Discuss the following series defined by the following formulas convergence.5. (7 points)According to ,calculate the exact valve of 6. (8 points)Weve known that ,please figure out the absolute maximum and minimum during the interval 0,7. (7 points)There is a function,f(x) is continuous at x=01find f(0) 2find the tangent line of f(x) when x=08. (9 points)Please find line L,if it pass through point (-1,-4,-3),and is perpendicular to9. (9 points)Find the