This function is given by 1(2.) = { (a) Find a formula for the single variable...

  

Transcribed Image Text:

This function is given by 1(2.) = { (a) Find a formula for the single variable function f(0, y) Try f(0.)- What is f(0,0) for this function? f(0,0)= Find its limitasy+0: lim f(0, y) PHO (z,y) (0,0) (z,y)=(0,0). (b) Based on your work in (a), is the single variable function f(0, y) continuous?? O f(0,0) lim f(a,0)= 4-0 (c) Next, similarly consider f(z,0). f(x,0) = (d) Based on this work in (a), is the single variable function f(x,0) continuous?? O (e) Finally, consider falong rays emanating from the origin. Note that these are given by y=mz, for some (constant) value of m. Find and simplify fon the ray ya f(x,x)= (Notice that this means that yis a contour of f. Be sure you can explain why this is.) Find and simplity on any ray y = m. f(x, m)- (Again, notice that this means that any ray y ma is a contour off; be sure you can explain why) () is f(z,y) continuous at (0,0)?? O This function is given by 1(2.) = { (a) Find a formula for the single variable function f(0, y) Try f(0.)- What is f(0,0) for this function? f(0,0)= Find its limitasy+0: lim f(0, y) PHO (z,y) (0,0) (z,y)=(0,0). (b) Based on your work in (a), is the single variable function f(0, y) continuous?? O f(0,0) lim f(a,0)= 4-0 (c) Next, similarly consider f(z,0). f(x,0) = (d) Based on this work in (a), is the single variable function f(x,0) continuous?? O (e) Finally, consider falong rays emanating from the origin. Note that these are given by y=mz, for some (constant) value of m. Find and simplify fon the ray ya f(x,x)= (Notice that this means that yis a contour of f. Be sure you can explain why this is.) Find and simplity on any ray y = m. f(x, m)- (Again, notice that this means that any ray y ma is a contour off; be sure you can explain why) () is f(z,y) continuous at (0,0)?? O