Use the method of your choice to evaluate the following limits. lim(x,y)→(1,1)x2+xy−2y22x2−xy−y2

Question

Use the method of your choice to evaluate the following limits.  lim(x,y)→(1,1)x2+xy−2y22x2−xy−y2

Dora · Accepted Answer

Given:  lim(x,y)→(1,1)x2+xy−2y22x2−xy−y2  To evaluate:  The given limit.  Solution:  Here,  lim(x,y)→(1,1)x2+xy−2y22x2−xy−y2  On simplifying the equation,  The required equation is,  lim(x,y)→(1,1)x2+xy−2y2x2−xy2−y2=lim(x,y)→(1,1)x+2y2x+y  Plug in the values (x,y)=(1,1)  lim(x,y)→(1,1)x2+xy−2y2x2−xy2−y2=1+2×12×1+1  lim(x,y)→(1,1)x2+xy−2y2x2−xy2−y2=1+22+1  lim(x,y)→(1,1)x2+xy−2y2x2−xy2−y2=33  lim(x,y)→(1,1)x2+xy−2y2x2−xy2−y2=1  Which is required.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Use the method of your choice to evaluate the following limits. lim(x,y)→(1,1)x2+xy−2y22x2−xy−y2

Answered question

Answer & Explanation