Question

A ball is hanging by a string from the ceiling of the roof draw a neat labelled diagram showing the forces acting on the ball and the string

Answer 1

Answer:

I have been trying to prove this formula for the limit of a sequence of the form

limn→∞(1+xn)n=ex

for any x

I started by taking the natural log of an to simplify the form to

nln(1+xn)=ln(1+xn)1n

Now if you take the limn→∞, we get the indeterminate form 00

So then by L'Hopital's rule, it becomes

1n4+xn3

and here I feel like I hit a dead end because we still can't get a limit.

Does anybody see a mistake I made? I am looking for some clues. Thanks.