Question

Please help find the limit (2 Variables)

lim(x,y) —> (0,0)

of

tan(x^2 +y^2)arctan(1/(x^2 +y^2))

Answer 1

have you tried just plugging in x,y = 0?

Answer 2

yes. but you will end up with tan(0)arctan(1/0)

Answer 3

can we use Lhopitals rule inside the arctan function

Answer 4

what is tan \((\pi /2) \) ??

Answer 5

sin(π/2)/cos(π/2)

Answer 6

also 1/0

Answer 7

tan pi/2 is undefined and then that behavious repeats itself meaning that arctan(1/0) is defined

so you have 0 x something finite = 0