Question: Please show all work, step by step. Thank you so much! 3xy2 5. (6 pts) Explain why lim doesn't exist. Hint! For one path consider

Please show all work, step by step. Thank you so much!

3xy2 5. (6 pts) Explain why lim doesn't exist. Hint! For one path consider x = yz. (x,y)-(0,0) x2 + y4Solution Given lim ( my ) - (010) using the hint choosing me= g2 path Step - 1 Replacing y? with 22 Now lim 3 ( ze ) ( DC ) ( m.) - (0 , 0 ) De2 + ( 2 ) 2 5 ) lim 3 2 2 2:30 - 10,0 ) Step - 2 let's take other path 8 = 20 lim 3 72 x X 2 = Jim 3 23 ( 2, n ) - (010 ) 212 + 2 4 5 ) lim 3 x 3 X0 (2 , 2) (0, 0 ) 1 + 2 2 O 170 Step - 3 Since for two different pathe we one getting two different limits Which should mot happen Hence limit as does not exist

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