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Let the function z = z(x,y) be determined by the equation f(x+mz,y+nz) =0, where f(u,v) is a differentiable function and m and n are constants, find m( z x) + n( z y).

Solution: According to the meaning of the topic, u=x+mz; v=y+nz；

z x=-[f u)( u x)+(f v)( shanmaihu v x)] f u) (u z)+(f v)( v z)]

(f/∂u)(1+m∂z/∂x)+(f/∂v)(n∂z/∂x)]/f/∂u)(m)+(f/∂v)(n)]

Go to the denominator. z x)[(m f u)+(n f v)]=gauge f u)(1+m z x)+(f v)(n z x)]=f u+(m f u+n f v)( z x)]

Shift: 2[(m f u)+(n f v)](z x)=-f u

Therefore f x=-(f u).1)

z/∂y=-[f/∂u)(∂u/∂y)+(f/∂v)(∂v/∂y)]/f/∂u)(∂u/∂z)+(f/∂v)(∂v/∂z)]

(f u)(m z y)+(f v)(1+n z y)] [( f u)(m)+(f v)(n)].

Go to the denominator. ∂z/∂y)[(m∂f/∂u)+(n∂f/∂v)]=f/∂u)(m∂z/∂y)+(f/∂v)(1+n∂z/∂y)]=f/∂v+(m∂f/∂u+n∂f/∂v)(∂z/∂x)]

Move the term to get 2[(m f u)+(n f v)](z y) = -f v

Therefore z y=-(f v)2)

m(∂z/∂x)+n(∂z/∂y)=-m(∂f/∂u)/-n(∂f/∂v)/

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I hope to be prepared for you to ruin your credit.

z x=- f socks x trouser leather f z other similarities Hu sleepy.

Hello: This question is still difficult.

Let the speed of A and B respectively, the distance between the two places of ab is s, firstly, according to the time of A and B after meeting is equal to 5 hours and the distance of A after meeting is a quarter of the whole journey, two equations can be listed: 1 4 (s + 45) divided by m = 5;3 4 (s+45) divided by n = 5

Then, according to the distance traveled by A and B after the encounter is related to S, the equation can be obtained: 5m+5n-45=s, then the three equations and three unknowns are OK.

However, I think you may have copied the wrong question, and there should be other conditions!

The numerator and denominator are multiplied by [ (1 x) 3] [cubic root number x 2 2 cubic root number x 4] to obtain:

[Cubic root number x 2 2 Cubic root number x 4] [ (1 x) 3].

The limit of this is equal to: 2

The numerator and denominator are derivatives at the same time.

1-x)^(1/2)-3)"=(1/2)(1-x)^(1/2-1)*(1)

2+x^(1/3))"=(1 3)(x (1 3-1)) with x=-8

So the original formula = (-1 2*(1+8) (1 2)) (1 2*(-8) (2 3)) = (-1 6) (1 8) = -4 3

Apply the Law of Lopida.

The numerator and denominator are derivatives respectively.

=lim( (1-x)-3).'/(2+x^1/3)'

1 2*(1-x) (1 2) [1 3*x (-2 3)]=-3 2*(1-x) (1 2) x (-2 3) substitute x=-8

The limit is -3 2*9 (-1 2) (-8) (2 3)=-3 2*1 3 (1 4)=-2

Already, x is a natural number, and x in turn represents an angle, 1) when x is the first.

1. The second image is time-limited, |sinx|Positive: f(x)=1 2(1+3)=22) when x is the first.

Three, four images are time-limited, |sinx|Negative: f(x)=1 2(-1+3)=1 The following is a discussion of x, which is a further difficulty.

There is no 0 non-state influence in the natural number, assuming that there is).

1) Medium: 0+2k(pi)=k=0, there is a value: 0,1,2,3;

When k=1, there is a value: . . Min closed answer.

Uh, then in (2): pi+2k(pi)=k=0, there are values: 4,5,6;

When k=1, there is a value: . .

You can find patterns and write sequences.

There's no requirement in the question.,I'm not going to get it.,Typing is too annoying.。

sinx !=0 x!=0

The number of sinx > is resistant to f(x)=2 when it is 0 (2k sinx< f(x)=1 at 0 (2k + x<2k +2 x belongs to the natural number, k belongs to the natural number of potato Hongchun).

[Idea Dialing].

1) Use the properties of the circumscribed quadrilateral in the circle to obtain d= ebc, and then use the mutual relationship to obtain gbe= ebc, and then find it;

2) first obtain d= abg, and then use the determination and properties of congruent triangles to obtain bce bge(asa), then ce=eg, and then use the properties of isosceles triangles to find it;