Why is 1∞ an indeterminate form while 0∞=0? If 0⋅0⋅0⋯=0 shouldn't 1⋅1⋅1⋯=1?
Answer
To say that 1∞ is an indeterminate form means that there is more than one object that can be limx→somethingf(x)g(x) where f(x)→1 and g(x)→∞, so that the limit depends on which functions f and g are.
Thus
limx→∞(1+1x)=1andlimx→∞(1+1x)x=eandlimx→∞(1−1x)=1andlimx→∞(1−1x)x=1e.}⟵two different numbers
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