Thursday, 27 July 2017

calculus - Indeterminate form 1infty vs. 0infty




Why is 1 an indeterminate form while 0=0? If 000=0 shouldn't 111=1?


Answer



To say that 1 is an indeterminate form means that there is more than one object that can be limxsomethingf(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(11x)=1andlimx(11x)x=1e.}two different numbers


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