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
The graph of a linear function is shown on the grid. (-3,3.6) (5,2) What is the rate of change of y with respect to x for this f
lilavasa [31]

Answer:

rate of change = -0.32

Step-by-step explanation:

Rate of change = slope,m

m =  \frac{y2 - y1}{x2 - x1}  \\ m =  \frac{3.6 - 2}{ - 3 - 2}  \\ m =  \frac{1.6}{ - 5}  \\ m =  \frac{ - 0.32}{1}

8 0
3 years ago
Read 2 more answers
Choose the expression that is equivalent to the expression
nadezda [96]

Answer:

A. n

Step-by-step explanation:

n/4 + n/4 + n/4 + n/4 = 4n/4 = n

4 0
3 years ago
Find the measure of Z CFD.СF5m + 116T3m + 80D
leva [86]
\begin{gathered} 5m+116+3m+80=180 \\ 8\text{m=180-116-80} \\ 8m=-16 \\ m=-2 \\ \text{CFD}=5m+116 \\ \text{CFD}=5\times(-2)+116 \\ \text{CFD}=-10+116 \\ \text{CFD}=106 \end{gathered}

7 0
10 months ago
HELP PLZ A bag contains 8 red marbles, 5 blue marbles, 4 green marbles,
mestny [16]

Answer:

is it multiple choice?

8 0
3 years ago
What is the value of X
kotegsom [21]

Answer:

x = 12√2

Step-by-step explanation:

This is a right triangle, which makes things easier.  Both legs have length 12.

Using the Pythagorean Theorem, we get x^2 = 12^2 + 12^2, or 2(144).

Solving for x, we get x = 12√2.

8 0
3 years ago
Other questions:
  • How does the graph of f(x)=1/2(3)^x+2-1 relate to its parent function?
    8·1 answer
  • Helppppppppppp plssss
    6·1 answer
  • Jade ha Jade has $451.89 in her checking account. After 3 checks, each for the same amount, are deducted from her account, she h
    10·1 answer
  • 6TH GRADE MATH SHOW WORK PLEASE
    5·2 answers
  • Plz help me with this
    15·1 answer
  • What is a prime factor?
    5·2 answers
  • Precal. Find the sum. Show every step you took to get to your answer. I will give brainliest if you are correct and show all wor
    12·1 answer
  • Can anyone help me with this?
    8·1 answer
  • I will give brainliest<br> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • Find the amount of simple interest earned for depositing the given principle in an account.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!