I am a professional calculus student while my friend's friend has just taken calculus I.
She says that 1∞ is one of the indeterminant forms and there is a special technique to solve it.
I told her, proceed please. She says:
Let
y=1∞=n→∞lim1n
elny=n→∞limeln1n
y=n→∞limenln1
y=elimn→∞nln1=elimn→∞0=e0=1
While her technique was not bad to solve limits to the power of n, I don't agree with her that 1∞ is one of the indereminant forms because we can always safely say 1∞=1.
From my long noob experience, I consider indeterminant form as a machine that will give us different numbers depending on the original argument of the limit where 1∞ is not the case here. Where did I go wrong with my conclusion?
She says that 1∞ is one of the indeterminant forms and there is a special technique to solve it.
I told her, proceed please. She says:
Let
y=1∞=n→∞lim1n
elny=n→∞limeln1n
y=n→∞limenln1
y=elimn→∞nln1=elimn→∞0=e0=1
While her technique was not bad to solve limits to the power of n, I don't agree with her that 1∞ is one of the indereminant forms because we can always safely say 1∞=1.
From my long noob experience, I consider indeterminant form as a machine that will give us different numbers depending on the original argument of the limit where 1∞ is not the case here. Where did I go wrong with my conclusion?