$f(x,y)=ln(\frac{19x^2-x^2y^2+19y^2}{x^2+y^2})$ is given as continuous function, so there exist $lim_{(x,y)\rightarrow(0,0)}f(x,y)$ and it is equal to f(0,0).

Put x=rcosA annd y=rsinA

$f(r,A)=ln(\frac{19r^2cos^2A-r^2cos^2A*r^2sin^2A+19r^2sin^2A}{r^cos^2A+r^2sin^2A})=ln(\frac{19r^2(cos^2A+sin^2A)-r^4cos^2Asin^a}{r^2(cos^2A+sin^2A)})$

we know that $cos^2A+sin^2A=1$ , so we have that

$f(r,A))=ln(\frac{19r^2-r^4cos^2Asin^a}{r^2})=ln(19-r^2cos^2Asin^2A)$

$lim_{(x,y)\rightarrow(0,0)}f(x,y)=lim_{r\rightarrow0}f(r,A)=ln19$

So f(0,0)=ln19.

8 0

2 years ago

Mario has drawn a plan of his bedroom on 1 cm square paper. His en-suite shower cubicle measure. 1m x1m, give the scale of his d

Romashka [77]

<span>Mario has drawn a plan of his bedroom on 1 cm square paper. His en-suite shower cubicle measure. 1m x1m, give the scale of his drawing
as ratio _ 1 cm__ : __1m_.
What are the actual dimension of his bed __1__ m x _1_ m</span>

4 0

2 years ago

Read 2 more answers

Find the coordinates of the point(s on the curve 2y=10?x2 that are closest to the origin

sergey [27]

No it far 10 is way out there

4 0

2 years ago

the price of gasoline varies directly with the number of gasoline purchased Purchase 15 gallons of gasoline you pay $36.75​

the price of gasoline varies directly with the number of gasoline purchased Purchase 15 gallons of gasoline you pay $36.75