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高等微积分考试代写 Advanced Calculus代写

2022-04-02 14:50 星期六 所属: 数学代写 浏览:143

高等微积分考试代写

Exam 1

高等微积分考试代写 You have an hour and 15 minutes for this test. Please show all reasoning; you may not get credit for answers which are not justified.

You have an hour and 15 minutes for this test. Please show all reasoning; you may not get credit for answers which are not justified. You may assume all results which have been given in class, in the book or in the homework. Since some problems are more difficult than others, please pace yourself so that you can try all of them. All problems have equal point value. Please do not use calculators. Good luck!

Points

(15)1.(a)For DB2 + C2 + D$ – 1 = 0, compute and  in terms of x,y,and z.  高等微积分考试代写

(b) Write down an expression for dz in terms of dx and dy

(15)  2.  Let 0 be a function from  to given by

高等微积分考试代写
高等微积分考试代写

Determine whether the limit  exists,and find its value if it does.Justify your answer either way.

(15)  3.  LetZ1=v1v2,z2=v1+v2,v1=u21+u2,v2=u22 From this find the matrix  as a product of two matrices, where Compute the value of this matrix at the values u1=1,u2=2.

高等微积分考试代写
高等微积分考试代写

(15) 4.Compute if x2u+v=0 and yv+xu=2  高等微积分考试代写

(20) 5.Consider the relationships x2+yu+xv=5 and xv+y2u.  Let dx = and

where dx ,dy,du,dv are the differentials of the variables.

(a)Compute if x,y are viewed as functions of u,v.

(b)At given fixed values for x=1,y=2,u=1,v=2 satisfying these relationships,

consider a matrix E such that dx = Adu. Find the top row (first 2 entries) of A.

(20) 6. Assume that the variables x,y,z, and w are related by a pair of equations. Assume that if we were to solve for z and w in terms of x and y, the partial derivatives would solve the equation    高等微积分考试代写

zx = wy.

Prove then that if we were to solve instead for z and x in terms of w and y, we would have

zw  = – xy

高等微积分考试代写
高等微积分考试代写

 

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