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(1) Massood Shawn ×Trump vs CNN FULLT A Sacramento Kings WeBW0rKf17bi ay: Mail massoodsat TO Archer's Chant Unlix > d webwork math ttu.edu/webwork2/f17bjayasi 2450s012/HW04/6/?user-msattan&key-F0yjoZHtyOE6AyJQS97d07QnK29Rvz008; effectiveUser-msattari WeBWorK Logged in as msattari. Log Out MATHEMATICAL ASSOCIATION OF AMERICA Kwebworkf17bijayasim2450s012 hw04 6 MAIN MENU Courses Homework Sets HW04: Problem 6 HW04 Problem 6 User Settings Grades Previous S Problem List Next (1 point) Find the limits, if they exist, or type DNE for any which do not exist. Problems 12:2 lim- 1) Along the a-axis: 4 2) Along the y-axis: 0 3) Along the line y-m 4) The limit is: DNE Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14... Problem 15.. Note: You can eam partial credit on this probiem Preview My Answers Submit Answers have attempted this problem 13 times. You Your overall recorded score is 50%. You have unlimited attempts remaining. Facebook Muska: Lol I always wonder how they detend his "grab em by the pussy" comment. Email instructo 8:57 PM ) Type here to search 26 10/6/2017Explanation / Answer
When we talk about finding the limit of a function of the form f(x,y) that is a function in two variables ,then the concept is the same as that in function of one variables , its just that we need to check if the function is continuous a the point in question or not.
i> Limit along the x - axis
Along the x axis all the y values are = 0 , so plug y = 0 and lets see what the limit becomes
lim (x,y --> 0,0) x^2/[4x^2 + y^2] = lim (x,y --> 0,0) = x^2/[4x^2 + (0)^2]
= lim (x,0 --> 0,0) = x^2/[4x^2] = 1/4
ii> Alony the y axis , along the y axis all the x values are = 0
=> lim (x,y --> 0,0) x^2/[4x^2 + y^2] = lim (0,y --> 0,0) (0)^2/[4(0)^2 + y^2]
= lim (0,y --> 0,0) 0/y^2 = 0
iii> Along the line y=mx , here m is a constant
here we'll plug y= mx in the given function, doing so well give us a function in one variable and from there we'll solve it as a limit of one variable function
lim (x,y --> 0,0) x^2/[4x^2 + y^2] = lim (x,y --> 0,0) x^2/[4x^2 + (mx)^2]
= lim (x,y --> 0,0) 1/[4 + m^2] = 1/(4+m^2)
iv> As we could see that the limit along the above three lines is not the same hence the limit of the function does not exist. DNE
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