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# 多变量微积分代写 MATH2720代写

2021-10-28 15:57 星期四 所属： 作业代写 浏览：24

## MATH2720 Multi-variable Calculus: Test Practice Pools

### Test 2 Practice Pool  多变量微积分代写

Disclaimer: There is no guarantee that your actual test questions will resemble these practice problems.

1. Let

(a)Finda ray approaching the origin along which f (x, y) = 1.

(b)Finda ray approaching the origin along which f (x, y) = 0.

(c)Whatcan we say about the limit of lim(x,y)(0,0) f (x, y)?

1. Evaluate ifpossible:

1. Evaluate each of the following limits or show that it does notexist:
1. Let

(a)Computefx using the defifinition.

(b)Computefy using the defifinition.

(c)Findd f (t, t)|t=0.

### 5.Findall first and second order partial derivatives of the following function and evaluate them at the given   多变量微积分代写

f (x, y, z) = ln(1 + exyz), (2, 0, 1).

1. Findall first and second order partial derivatives of the following function and evaluate them at the given

1. Letf be any differentiable function of one  Define z f (x2 + y2). Does the equation

always hold?

yzx xzy = 0

1. Letw f (x, y, t) with x and y depending on  Suppose that at some point (x, y) and at some time t, the partial derivatives fx, fy, ft are equal  多变量微积分代写

to 2,3,and 5 respectively, while  what is dw ? Is it the same with ft? why or why not?

1. Evaluatews and wt given w x2 + y2 + z2, x st, y s cos t, z s sint
2. Suppose x2y +z = 1. Let w = sin x cos(2y). Find

### 11.LetfFind the equation of tangent plane to the surface z = f(x, y) at (−1, 1, 1 ). 多变量微积分代写

1. Consider the surface z = f (x, y) defined implicitly by the equation xyz2+ y2z3 = 3 + x2. Use a 3–dimensional gradient vector to find the equation of the tangent plane to this surface at the point (1, 1, 2).
2. Findall horizontal planes that are tangent to the surface with equation z xye(x  +y  )/2.

14.Find the directional derivative of f (x, y, z) = exyzin the direction of (0, 1, 1) at (0, 1, 1).  多变量微积分代写

1. Let z = (y2x2)2. Find all critical points of z. Identify whether they are local minimum, local maximum or saddle points.

16.: Find all critical points for f (x, y) = x(x2+ xy + y2 9). Also find out which of these points give local maximum values for f(x, y), which give local minimum values, and which give saddle points.

17.Use the Second Derivative Test to find all values of the constant c for whichthe function z x2 + cxy y2 has a saddle point at (0, 0).

18.Findthe maximum and minimum values of f (x, y) = xy  x3y2when (x,y) runs over the square 0 x 1, 0 y 1.