How can I show this...

[DavidHooper]

f(R)=R - (R^2) / (R+h)
h is some small constant.

Show that as R --> infinity then f(R) --> h.

[Destined Soul]

I'm somewhat rusty at my limits, etc, but here goes. Spot the mistakes, if you want. :P

R - (R^2)/(R+h). Give both a common denominator.

Which gives (R^2 + Rh - R^2) / (R+h) = (Rh)/(R+h)

Factor out h's on top and bottom, yields:

R / (R/h + 1). Doubly inverted, this is:

1 / ( (R/h+1) / R ) = 1 / (1/h + 1/R)

When R -> Infinity, 1/R -> 0, so we end up with 1 / (1/h) = h.

I hope this is right.

Destined

[unformed]

destined soul is correct....

[Lior]

Its pretty simple:

X - (X²)/(X+h) acctually means:

(X²+hX-X²) / (X+h) which means:

hX / (X+h)

Now:

Lim (hX / (X+h)) when X-->infinite gives h/1 which is h.

Because the exponents of the X is equal in both the numerator and denominator.

Then you just have to calculate now how much is the coefficient of the X in the numerator devided by the coefficient of the X in the denominator.

This gives you h/1 which is h.

Hope this helps.