I just start learning about error theory, rounding etc. Concerning the solution, we need to find the absolute error of the function $\Delta_{z^*}$ and then use it to find the number of true significant figures $ \Delta_{z^*} \leq 0,5\cdot10^{n-m+1}$
My doubts and questions:
(1) Do $e$ , $\sin$ ,$\ln$ also induce error into the absolute error of our function? My guess is that yes. My teacher just told me to take up to 3-4 decimals of $e$ How do we determine how many decimals of $e$ should we take?
(2) My teacher told me to find $\Delta_{z^*}$ using partial derivates. Personally,for this function, I find it unpractical and tedious. On the comments somebody suggested using Taylor series in Maclaurin form, I do not get how to implement it in this problem. In fact $ \Delta_{z^*}= \left|\displaystyle \sum_{i=1}^{\infty} \frac{\partial f(x^*)}{\partial x_i}\right|\Delta_{x_i^*}$ somehow resembles the Taylor expansions. Is there a more practical method for finding $\Delta_{z^*}$
- Given $x=8.34 \pm 0.005 ; y=7.2 \pm 0.05$. Calculate $$ z=\frac{\sin (3 x+0.7 y)}{\mathrm{e}^{0.4 x+0.5 y}} \cdot(7 x+\ln y) $$ and determine the number of true significant digits in the product.