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julsineya [31]
4 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]4 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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ASAP
pav-90 [236]

Answer:

+ 2 is a value for "C"

if the general form is ax^2 + bx +c and you want the A to be a positive integer...

then the c value would be -8

3x^2 - 8 = 0

Step-by-step explanation:

3 0
3 years ago
How do i solve for x 30x - 60 = 20x
Lena [83]
First, subtract 30x from each side to get:
-60 = -10x
Then, divide each side by -10 to get:
x = 6
Now, plug back in to check your answer:
30(6) - 60 = 20(6)
180 - 60 = 120
120 = 120

Hope this helps!! :)
4 0
3 years ago
You spin the spinner below once. What is the sample space?
masya89 [10]
The answer is the 3rd one.
4 0
3 years ago
Find the missing values of the variables. The diagram is not to scale.
julsineya [31]

X=93 degrees

Y=74 degrees

3 0
3 years ago
1. A sample consists of 75 TV sets purchased several years ago. The replacement times of those TV sets have a mean of 8.2 years.
Greeley [361]

Answer:

8.2+/-0.25

= ( 7.95, 8.45) years

the 95% confidence interval (a,b) = (7.95, 8.45) years

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 8.2 years

Standard deviation r = 1.1 years

Number of samples n = 75

Confidence interval = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

8.2+/-1.96(1.1/√75)

8.2+/-1.96(0.127017059221)

8.2+/-0.248953436074

8.2+/-0.25

= ( 7.95, 8.45)

Therefore the 95% confidence interval (a,b) = (7.95, 8.45) years

3 0
3 years ago
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