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Answers
Infinity is a concept, not a Real Number.
"0 x infinity" is a concept in Real Analysis, where we multiply two functions one of which F1 tends to 0 and another F2 tends a large number without limit (commonly considered Infinity) and the multiplication F1*F2 is another function which may have a Definite number, but we can not say what "0 x infinity" is without knowing F1 and F2. So we can not Define "0 x infinity" as 1 or 2 or 4 or whatever. We must know F1 and F2 to find the answer.
In below examples, I use "=" as a short form for "tends to".
Eg, F1=x, and F2=1/x. When "X tends to 0" or "X=0", F1=0, & F2=Infinity. But "0 x infinity" = x*(1/x)=1.
Eg, F1=x, and F2=2/x. When X=0, F1=0, & F2=Infinity. But "0 x infinity" = x*(2/x)=2.
Eg, F1=sin(x), and F2=1/tan(x). When X=0, F1=0, & F2=Infinity. But "0 x infinity" = sin(x)/tan(x)=sin(x)/(sin(x)/cos(x))=cos(x)=cos(x)=1.
Eg, F1=x^2, and F2=2/x. When X=0, F1=0, & F2=Infinity. But "0 x infinity" = x^2*(2/x)=x/2=0.
Basically, "0 x infinity" is InDeterminate, because we can not fix the value without knowing which "0" and which "infinity".
Answer:
0 is ur answer
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