Consider f defined by

f(x, y) =

[aln(z²+3y²),

a

10

a. Find f, for all (x, y) = (0,0).

f. =

sin (a)

Oz

⠀⠀

if (x, y) = (0,0)

if (x, y) = (0,0)

[1 point]

b. Is f, is defined for (0,0)?

Of, is defined

O f₂ is not defined

[0.5 point]

c. Is f, defined for all (x, y) = R²?

O f, is defined

Ofy is not defined

[0.5 point]

C

E

~/nd. For (x, y) (0,0), fy=

Ta

P

sin (a)

8

R

C:

[1 point]

e. For (x, y) = (0,0), fy=

[1 point]

f. In the previous parts, we have seen that fy is

defined for all (x, y) = R2. This means the partial

derivative f, is defined for (0,0). Does

that imply f, is continuous at (0,0)?

Of is continuous at (0,0)

O fy is not continuous at (0,0)

[2 point]