1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alexxandr [17]
3 years ago
5

Define f(0,0) in a way that extends f to be continuous at the origin. f(x, y) = ln ( 19x^2 - x^2y^2 + 19 y^2/ x^2 + y^2) Let f (

0,0) be defined to be .
Mathematics
1 answer:
kirill115 [55]3 years ago
8 0

Answer:

f(0,0)=ln19

Step-by-step explanation:

f(x,y)=ln(\frac{19x^2-x^2y^2+19y^2}{x^2+y^2}) is given as continuous function, so there exist lim_{(x,y)\rightarrow(0,0)}f(x,y) and it is equal to f(0,0).

Put x=rcosA annd y=rsinA

f(r,A)=ln(\frac{19r^2cos^2A-r^2cos^2A*r^2sin^2A+19r^2sin^2A}{r^cos^2A+r^2sin^2A})=ln(\frac{19r^2(cos^2A+sin^2A)-r^4cos^2Asin^a}{r^2(cos^2A+sin^2A)})

we know that cos^2A+sin^2A=1, so we have that

f(r,A))=ln(\frac{19r^2-r^4cos^2Asin^a}{r^2})=ln(19-r^2cos^2Asin^2A)

lim_{(x,y)\rightarrow(0,0)}f(x,y)=lim_{r\rightarrow0}f(r,A)=ln19

So f(0,0)=ln19.

You might be interested in
Plz help me with this problem
mixer [17]
I don’t know what is your problem is
7 0
3 years ago
Nine tenths of the grade 9 class are in the gym. If these students are divided into three equal groups, what fraction of the cla
Dahasolnce [82]
Times by 3. Then divide the top backup by 3 to get 9/30. 9/30+9/30+9/30=27/30=9/10.
3 0
3 years ago
The rate at which velocity changes is called A)acceleration B)speed C)direction D)displacement
PolarNik [594]
Acceleration is the answer
4 0
3 years ago
Read 2 more answers
What is the means-to-MAD ratio of the two data sets, expressed as a decimal to the nearest tenth?
FinnZ [79.3K]
Frist we need to find the mean of both so 

1.55

2.67

then we make a number graph and see how mant place does it take to get to them from 0 67and55/by them selfs = 1.2(rounded)

1.2 is you answer

4 0
3 years ago
HELP ME PLSSSSSS<br><br> if f(x) = 2x-3/5 , which of the following is the inverse of f(x)?
neonofarm [45]
The answer is (5x+3)/2 . So it’s A .
8 0
2 years ago
Other questions:
  • The function f(x) = RootIndex 3 StartRoot x EndRoot is reflected over the x-axis to create the graph of g(x) = Negative RootInde
    10·1 answer
  • What is (14.2a + 9.8b) - (13.1b - 0.2a) - (3.7a + 4.8b) simplified
    10·1 answer
  • 2x - 7y = 2 and 3x + y = -20 addition/elimination
    10·1 answer
  • Help please!! thank you
    14·1 answer
  • Round 16051 to thousand
    14·1 answer
  • Please help i am in class and need help pleaseeeeee​
    14·1 answer
  • Solve the following equation<br>7/3x=5​
    9·2 answers
  • -25.63+ -30.59 ??? Can someone let me know what this equals?
    13·2 answers
  • <img src="https://tex.z-dn.net/?f=%5Csqrt%5Cfrac%7B9%7D%7Bx-4%7D" id="TexFormula1" title="\sqrt\frac{9}{x-4}" alt="\sqrt\frac{9}
    7·1 answer
  • the students in Mrs. Aubrey's class brought in 15 cans during week 1 of the food drive. during week 2 the students brought in 4
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!