If f(x) and g(x) are such that lim f(x) as x --> a = + infinity and lim g(x) as x --> a = 0 Then
lim [ f(x) . g(x) ] as x --> a is always equal to 0
lim [ f(x) . g(x) ] as x --> a is never equal to 0
lim [ f(x) . g(x) ] as x --> a may be +infinity or -infinity
lim [ f(x) . g(x) ] as x --> a may be equal to a finite value