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joannachavez12345
joannachavez12345
26.02.2020 • 
Mathematics

(1 point) Examine the behavior of f(x,y)=9x2.25x2+y2f(x,y)=9x2.25x2+y2 as (x,y)(x,y) approaches (0,0)(0,0). (a) Changing to polar coordinates, we find lim(x,y)→(0,0)(9x2.25x2+y2)=limr→0+, θ=anything(lim(x,y)→(0,0)(9x2.25x2+y2)=limr→0+, θ=anything( )=)= . Use "theta" for θθ. Use "infinity" for "[infinity][infinity]" and "-infinity" for "−[infinity]−[infinity]". Use "DNE" for "Does not exist". (b) Since f(0,0)f(0,0) is undefined, ff has a discontinuity at (x,y)=(0,0)(x,y)=(0,0). Is it possible to define a function g:R2→Rg:R2→R such that g(x,y)=f(x,y)g(x,y)=f(x,y) for all (x,y)≠(0,0)(x,y)≠(0,0) and gg is continuous everywhere? If so, what would the value of g(0,0)g(0,0) be? If there is no continuous function gg, enter DNE. g(0,0)=g(0,0)=

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