Looking through my old calc notes, I am reading that f(x) needs to be continuous on [a,b] and f ' (x) also needs to be continuous on [a,b]. Both conditions are needed. If you had to pick just one, then I'd say f(x) being continuous is much more important. Though I'm not 100% sure on this one. My thinking is that if there was any discontinuities on f(x), then the arc length would be distorted and overblown. The arc length should not account for any piece that isn't on the curve.
Answer:
4
45×4=180
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Answer:
The greater the sample size the better is the estimation. A large sample leads to a more accurate result.
Step-by-step explanation:
Consider the table representing the number of heads and tails for all the number of tosses:
Number of tosses n (HEADS) n (TAILS) Ratio
10 3 7 3 : 7
30 14 16 7 : 8
100 60 40 3 : 2
Compute probability of heads for the tosses as follows:

The probability of heads in case of 10 tosses of a coin is -0.20 away from 50/50.

The probability of heads in case of 30 tosses of a coin is -0.033 away from 50/50.

The probability of heads in case of 100 tosses of a coin is 0.10 away from 50/50.
As it can be seen from the above explanation, that as the sample size is increasing the distance between the expected and observed proportion is decreasing.
This happens because, the greater the sample size the better is the estimation. A large sample leads to a more accurate result.