I'm new to vector calculus, and I'm working on schaum's vector analysis book. So far, I've solved many problems without getting stuck. However, this problem is bugging me.
It's asking for T, N, B , κ and .
x= arctan (s), y= $1/2(√2)(s^2+1)$ , z= 1-arctan (s)
I've worked through the problem normally and got T = $\frac {\hat{i}+s^2\hat{k}}{s^2+1}√2*s\hat{j}$, , and the rest is derived from this. However, the book's solution is T= $\frac {\hat{i}+√2*s\hat{j}+s^2\hat{k}}{s^2+1}$.
Did I do something wrong here?
I think that you should write the problem as stated in the book. And the problem (problem 48, p. 55) is about $c(s)=\bigl(x(s),y(s),z(s)\bigr)$, where$$x(t)=\arctan s\text{, }y(s)=\frac{\sqrt2}2\ln\bigl(s^2+1\bigr)\text{ and }z(s)=s-\arctan(s).$$So$$T(s)=c'(s)=\frac1{1+s^2}\left(1,\sqrt2\,s,s^2\right),$$which is the answer provided by the book.