Question

Continuity Problem!

Answer 1

\[f_x = \frac{ -\cos(x)\sin(x) }{ \sqrt{\cos^2(x)+y} }\]
and
\[f_y=\frac{ 1 }{ 2\sqrt{y+\cos^2(x)} }\]

Answer 2

Both \[f_x and f_y\] are continuous functions for y > ?_?

Answer 3

I said 0, but it is still incorrect.

Answer 4

if it were continuous for y=0 then with x=pi/2 you would have 0 in the denominator

Answer 5

If y is greater than -1 the denominator cannot be 0. Which I assumed is the continuous part.

Answer 6

oh i see you said y>0
well cos^2 can't be <0

Answer 7

yes, so I thought y > 0. y greater than 0 would be all numbers larger than 0, which would make the denominator not 0.

Answer 8

Both f_x and f_y are continous functions for y > blank.

Answer 9

I have entered 0, cos^2x, -2,-1.

Answer 10

yeah I'm having a hard time seeing how you are wrong as well :P

Answer 11

thank you!

Answer 12

i did the rest of the problem, it's just that.

Answer 13

oh how quickly my multivariable skills fail me :(

Answer 14

trig an algebraic expression are continuous on their domain

I would say \(y>-\cos^2(x)\)

Answer 15

oh, what about just solving y+cos^2x=0 ?

Answer 16

yeah, but you didn't try the solution to y+cos^2x>0 as an answer

Answer 17

y+cos^2x>0
y> ???

Answer 18

I am so silly, you're right thank you guys! For cracking the code!