- #1
Nusc
- 760
- 2
y=kcosh(x/k) = k(e^(x/w) + e^(-x/k))
y ~ k[1 + x/k + (1/2!)(x^2/k^2) + (1/3!)(x^3/k^3)] +...+ k[1 - x/k +(1/2!)(x^2/k^2) - (1/3!)(x^3/k^3) +...]
All odd terms except 1 cancel out.
So we are left with
y = k [2 + (2/2!)(x^2/k^2) + (2/4!)(x^4/k^4) + (2/6!)(x^6/k^6) +...]
I've been staring at this for hours and I'm supposed to show that:
y= k + (1/2k)(x^2) for k>>x
What did I do wrong? My error lies somewhere where the twos are bolded.
y ~ k[1 + x/k + (1/2!)(x^2/k^2) + (1/3!)(x^3/k^3)] +...+ k[1 - x/k +(1/2!)(x^2/k^2) - (1/3!)(x^3/k^3) +...]
All odd terms except 1 cancel out.
So we are left with
y = k [2 + (2/2!)(x^2/k^2) + (2/4!)(x^4/k^4) + (2/6!)(x^6/k^6) +...]
I've been staring at this for hours and I'm supposed to show that:
y= k + (1/2k)(x^2) for k>>x
What did I do wrong? My error lies somewhere where the twos are bolded.