f(R)=R - (R^2) / (R+h)
h is some small constant.
Show that as R --> infinity then f(R) --> h.
Printable View
f(R)=R - (R^2) / (R+h)
h is some small constant.
Show that as R --> infinity then f(R) --> h.
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
destined soul is correct....:)
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.