Taylor Series

3. Taylor Series
Exercise 1
As N increases, the number of oscillations in the Taylor series increases.






Exercise 2


Just to the right of x=2, the graph for Tn(x) drops down abruptly if N is an even integer and goes up when N is an odd integer. Instead of increasing the number of oscillations, as N increases the Taylor series at x=2 changes from going up to going down.
Exercise 4
taylor(log(v), v, 5, 1)
ans = v-1-1/2*(v-1)^2+1/3*(v-1)^3-1/4*(v-1)^4
>> pretty(ans)
2 3 2 4
pi k T v pi h v pi h v
8 --------- - 4 ------- + 2/3 --------
...