- #1

willy0625

- 6

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## Homework Statement

How would you go about proving that the functions

[tex] F(x)=\frac{2}{\pi}\arctan\Big(\frac{x}{a}\Big), x \geq 0[/tex]

with [tex]a > 0[/tex]

and

[tex] G(x)=1-\exp(-\lambda x),x\geq0[/tex]

with [tex]\lambda>0[/tex]

meet only at one point for some [tex] x > 0 [/tex]

## The Attempt at a Solution

At [tex]x=0[/tex], F and G takes the values 0s and both of the functions tend to 1 when x gets really large I think they must meet at least once. But still not sure about finding the actual point(s) since i do not think i can solve the equation

[tex]F=G[/tex] analytically.

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