Evaluate the limit, if it exists, or show that the limit does not exist. (a) lim (x, y)→(0,0) 5x + y √ 5x + y + 9 − 3 (b) lim (x, y)→(0,0) 2xy x 2 + y 2

Step-by-step explanation:

GIven that :

(a) lim (x,y)→(0,0) 5x + y √ 5x + y + 9 − 3

(b) lim (x,y)→(0,0) 2xy x 2 + y 2

We are to evaluate and determine if the limit exist or not.

From (a);

x = 0

y = 0    (Since no presence of indeterminate)

=

= 0+0+0 +9 - 3

= 6

Therefore; the limit exist

(b)

If  y = mx

So;  the limit depends  on the value of m; then the limit does not exist

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no, because the sides are not congruent