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julsineya [31]
3 years ago
9

1. By considering different paths of approach, show that the function has no limit as (x, y) -------> (0, 0).

Mathematics
1 answer:
solmaris [256]3 years ago
7 0

Answer:

1. shown below

2. \frac{-1}{\sqrt{2}}

Step-by-step explanation:

We say \displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y) exists if the limit remains the same along every path.

Here, f is a function on two variables defined on a disk that contains the point (a,b).

1.

Along y-axis i.e., x = 0:

\displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y)=\displaystyle \lim_{(x,y)\rightarrow (0,0)}\frac{-x}{\sqrt{x^2+y^2}}=\displaystyle \lim_{y\rightarrow 0}\frac{0}{\sqrt{0^2+y^2}}=0

Along x-axis i.e., y = 0:

\displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y)=\displaystyle \lim_{(x,y)\rightarrow (0,0)}\frac{-x}{\sqrt{x^2+y^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{\sqrt{x^2+0^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{x}=-1

As the limit is not the same along different paths, so limit does not exist.

2.

Along the path x = y:

\displaystyle \lim_{(x,y)\rightarrow (a,b)}f(x,y)=\displaystyle \lim_{(x,y)\rightarrow (0,0)}\frac{-x}{\sqrt{x^2+y^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{\sqrt{x^2+x^2}}=\displaystyle \lim_{x\rightarrow 0}\frac{-x}{\sqrt{2}x}=\frac{-1}{\sqrt{2}}

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m_a_m_a [10]

Answer:

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Step-by-step explanation:

1) What is the solution of the given system?

5x-y=-7

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Multiply the second equation by -1

-1*(3x-y)=-1(-2)

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Now add the first equation to the modified second equation

5x-y=-7

-3x +y = 2

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2x = -5

Divide each side by 2

2x/2 = -5/2

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Subtract 7.5 from each side

7.5 -7.5 +y =2-7.5

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2) what is the solution of the given system?

5x+7y=32

8x+6y=46

Divide the second equation by 2

8x/2+6y/2=46/2

4x+3y =23


Multiply the first equation by 4

4 (5x+7y)=32*4

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Now multiply the modified 2nd equation by -5

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Lets add the new equations together to eliminate x

20x+28y = 128

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Divide each side by 13

13y/13 =13/13

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5x +7 =32

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alex41 [277]
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We continue calculating 6% then adding that onto the total before calculating it for the next year for problem B.
6% of $44,944 is $2,696.64. $44,944+$2,696.64=$47,640.64.
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Hopefully you can figure out C on your own! I feel a little bad for giving a partial answer but I think you can do this!

Percentage calculator used-https://percentagecalculator.net/
Note: can't handle commas, remove all commas before entering data in.
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