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forsale [732]
2 years ago
10

Which condition must be satisfied in order to use the arc length formula L = the integral from a to b of sqrt(1 + f'(x)^2) dx?

Mathematics
1 answer:
ivanzaharov [21]2 years ago
6 0
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. 
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Answer:

Therefore m_{2} = -3.

Step-by-step explanation:

i) let us say the slope of the line passing through (-2,7) and (4,9) is m_{1}.

ii) to find the slope of the line passing through two points (x_{1}, y_{1}) and (x_{2},y_{2}) we use the formula m = \dfrac{y_{2} - y_{1} }{x_{2}  - x_{1} }. Therefore we can say that  m_{1} = \dfrac{9 - 7}{4 - (-2)} = \dfrac{1}{3}.

iii) let us say the slope of the perpendicular line to the line  passing through (-2,7) and (4,9) is m_{2}

iv) from the formula for the slopes of a line and the line perpendicular to it which is given by m_{1} × m_{2} = -1, therefore m_{2} = -1 ÷  m_{1} = -3. Therefore m_{2} = -3

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Step-by-step explanation:

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