Question

find the limit, if it exists, or show that the limit does not exist

Answer 1

limit (x,y)--->(0,0) xy^2cosy/x^2+y^4

Answer 2

i did the y path where x=0 and i got lim (0,y)--->(0,0) cosy/y^4

Answer 3

try \[y=\sqrt{x}\]

Answer 4

okay let see

Answer 5

i got (x^2*cosy)/2x^2

Answer 6

yes...simplify and take the limit

Answer 7

okay i got lim y-->0 cos(0)/2 = 1/2

Answer 8

and what did you get as a final answer when you let x=0

Answer 9

i got 1/0

Answer 10

no

Answer 11

its wrong?

Answer 12

i made a mistake its 0

Answer 13

\[\frac{xy^2\cos(y)}{x^2+y^4}\]

let x=0

\[\frac{0y^2\cos(y)}{0^2+y^4}\]

\[=\frac{0}{y^4}=0\] for all y not zero

Answer 14

good...is 0 equal to 1/2

Answer 15

nope so its DNE

Answer 16

correct

Answer 17

thank you

Answer 18

@Zarkon how did you know to use y=sqrt(x)? is there something that tells what to use?

Answer 19

it made the denominator have two x's that had the same power so I could combine them...among other things