robertdeniro
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Homework Statement
f(x)=\frac{e^{x}-e^{-\sqrt{x}}}{e^{\sqrt{x}}-e^{-\sqrt{x}}}
show f(0)=1/2
Homework Equations
The Attempt at a Solution
Last edited:
fzero said:I think you have a sign wrong somewhere, otherwise the LHS = 1. But if you can express your equation in the form
e^{\sqrt{x}} = A e^x
you can take a logarithm of both sides to get a more manageble equation to solve.
fzero said:You added "Show f(0) = 1/2" but you haven't defined f(x).
robertdeniro said:fixed that too
fzero said:OK, the image probably didn't reload in my browser.
Have you tried taking the limit as x\rightarrow 0? You should really show some of your work before asking for help.
fzero said:I think it helps to note that you can rewrite
<br /> f(x)=\frac{e^{x+\sqrt{x}}-1}{e^{2\sqrt{x}}-1}.<br />
Then you can factor the denominator and you get an expression where you can use L'Hopital on an indeterminant factor.
fzero said:Write that as a product of two factors, one of which is well-defined in the limit and the other which is indeterminate. L'Hopital can be applied to the indeterminate factor.
robertdeniro said:ok i see
but we evaluate its limit going to 0, but not AT 0.
i do not recall a theorem that says limit=actual value
robertdeniro said:Homework Statement
f(x)=\frac{e^{x}-e^{-\sqrt{x}}}{e^{\sqrt{x}}-e^{-\sqrt{x}}}
show f(0)=1/2
Homework Equations
The Attempt at a Solution