Hi all.
Have a BIG test tomorrow and I am puzzed at a math thing. Why is 2 the limit of x*(e^(2/x)-1)?
At least thats what mathematica says and I want to understand why. I mean, I have noticed a pattern.
x*(e^(2/x)-1) -> 2 when x->infinity
x*(e^(3/x)-1)-> 3 when x->infinity
x*(e^(4/x)-1) -> 4 when x->infinity
x*(e^(5/x)-1) -> 5 when x->infinity
...
x*(e^(2382/x)-1) -> 2382 when x->infinity
It seems like x*(e^(a/x)-1)-> a when x->infinity.
Why?
Take care,
Kerr.
Have a BIG test tomorrow and I am puzzed at a math thing. Why is 2 the limit of x*(e^(2/x)-1)?
At least thats what mathematica says and I want to understand why. I mean, I have noticed a pattern.
x*(e^(2/x)-1) -> 2 when x->infinity
x*(e^(3/x)-1)-> 3 when x->infinity
x*(e^(4/x)-1) -> 4 when x->infinity
x*(e^(5/x)-1) -> 5 when x->infinity
...
x*(e^(2382/x)-1) -> 2382 when x->infinity
It seems like x*(e^(a/x)-1)-> a when x->infinity.
Why?
Take care,
Kerr.