Find out the domain of function - three dimensional space, Mathematics

Assignment Help:

Find out the domain of each of the following.

 (a) f (x,y) = √ (x+y)

(b) f (x,y) = √x+√y

 (c) f (x,y) = ln (9 - x2 - 9y2)

Solution

(a) In this example we know that we cannot take the square root of a negative number thus this means that we must need,

x + y > 0

 Here is a diagram of the graph of this region.

 

803_Find out the domain of Function - Three Dimensional Space 3.png

(b) This function is not same from the function in the previous part.  Here we must need that,

 x ≥ 0   and  y ≥ 0

 and they actually do need to be separate inequalities. There is one for every square root in the function. 

Here is the diagarm of this region.

808_Find out the domain of Function - Three Dimensional Space 2.png

(c) In this last part we are familiar with that we cannot take the logarithm of a negative number or zero (0). Hence we need to require that,

9 - x2 - 9y2 > 0                  ⇒ x2 /9 + y2 < 1

and on rearranging we see that we require to stay interior to an ellipse for this function.

Here is a diagram of this region.

152_Find out the domain of Function - Three Dimensional Space 1.png


Related Discussions:- Find out the domain of function - three dimensional space

Business applications, Business Applications In this section let's tak...

Business Applications In this section let's take a look at some applications of derivatives in the business world.  For the most of the part these are actually applications wh

Airthmetic progression series, Each of the series 3+5+7+..... and 4+7+10......

Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co

Statistics, explain the characteristics of statistics

explain the characteristics of statistics

What is equivalent of this temperature in degrees fahrenheit, The temperatu...

The temperature in Hillsville was 20° Celsius. What is the equivalent of this temperature in degrees Fahrenheit? This problem translates to the expression 3 {[2 - (-7 + 6)] + 4

Do yall, do yall help kids in 6th grade

do yall help kids in 6th grade

Class limits and class boundries, Class limits These are numerical va...

Class limits These are numerical values, which limits uq extended of a given class that is all the observations in a provided class are expected to fall in the interval which

Mean, a data set has a mean of 3, a median of4, and a mode of 5, which numb...

a data set has a mean of 3, a median of4, and a mode of 5, which number must be in the data set 3,4,or5

Perimeter, what is the perimeter of a rhombus

what is the perimeter of a rhombus

Arclength surprise - mathematics, Suppose a unit circle, and any arc S on t...

Suppose a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is provided, the area between S and the x-axis plus the covered area between S and

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd