Nonexistence of a limit Investiage the limit lim_((x,y)->(0,0)) (x+y)^2/(x^2+y^2)

Jason Farmer 2021-01-31 Answered
Nonexistence of a limit Investiage the limit lim(x,y)(0,0)(x+y)2x2+y2
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

pivonie8
Answered 2021-02-01 Author has 91 answers
By applying identity (a+b)2=(a2+b2+2ab)
lim(x,y)(0,0)(x+y)2x2+y2=lim(x,y)(0,0)x2+y2+2xyx2+y2
lim(x,y)(0,0)(x+y)2x2+y2=lim(x,y)(0,0)x2+y2x2+y2+2xyx2+y2
lim(x,y)(0,0)(x+y)2x2+y2=lim(x,y)(0,0)x2+y2x2+y2+lim(x,y)(0,0)2xyx2+y2
lim(x,y)(0,0)(x+y)2x2+y2=lim(x,y)(0,0)1+lim(x,y)(0,0)2xyx2+y2
lim(x,y)(0,0)(x+y)2x2+y2=1+0
lim(x,y)(0,0)(x+y)2x2+y2=1
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-08
Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
P(x)=12x2+2136x41000
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?
asked 2021-02-05
Use polar coordinates to find the limit. [Hint: Let x=rcosandy=rsin , and note that (x, y) (0, 0) implies r 0.] lim(x,y)(0,0)x2y2x2+y2
asked 2021-09-13
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of 100+1003i
asked 2021-11-22
A large number N of people are subjected to a blood investigation. This investigation can be organized in two ways.
(1) The blood of each person is investigated separately. In this case N analyses are needed.
(2) The blood of k people are mixed and the mixture is analysed. If the result is negative, then this single analysis is sufficient for k persons. But if it is positive, then the blood of each one must be subsequently investigated separately, and in toto for k people, k + 1 analysis are needed. It is assumed that the probability of a positive result (p) is the same for all people and that the results of the analysis are independent in the probabilistic sense.
What is the probability that the analysis of the mixed blood of k people is positive?
What is the expectation of the number of analysis necessary in the second method of testing?
For what k is the minimum expected number of necessary analysis attained?"
asked 2021-09-12
Which of the following is true?
dydt+y1t=3t+4 is best solved with undetermined coefficients.
dydt=tyyt2 is best solved with separation of variables.
dydt=ty is best solved with integrating factors.
dydt=2ysin(5t) is best solved with separation of variables.
dydt=tyyt2 is best solved with undetermined coefficients.
asked 2021-09-08

Write an equation describing the relationship of the given variables.
y varies directly as the fourth power of x and when x=3,y=648

asked 2022-05-02
Solve for x: 0=-4u-7x+4.