All categories

3 years ago

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]3 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.

You might be interested in

What is the slope of the line that is perpendicular to the line that passes through (-2, 7) and (4, 9)? Type a numerical answer

kodGreya [7K]

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

6 0

3 years ago

Reuben runs 5 miles in 30 minutes. How many miles does he run per minute?

Irina18 [472]

1/6 of a mile per minute

8 0

2 years ago

HELPP will give Brainlyest answer!!!

nika2105 [10]

Answer:

Step-by-step explanation:

here you go!!

3 0

2 years ago

Someone please help me! I’ll give brainliest

Katarina [22]

Answer:

Step-by-step explanation:

3 0

3 years ago

The weight of an object on the moon is

Tanzania [10]

Answer:

40 2/5Ibs or $40\frac{2}{5}$ lbs

Step-by-step explanation:

Let weight of object on the moon be represented = Wm

weight of object on the Earth = We

In the above question, we are told:

The weight of an object on the moon is

5 of its weight on Earth.

Hence, mathematically, this is represented as:

5Wm = We

If a moon rock weighs 202 lbs on Earth

5Wm = 202lbs

Wm = 202lbs/5

Wm = $40\frac{2}{5}$ Ibs

Therefore, the moon rock weighs $40\frac{2}{5}$ Ibs on the moon.

7 0

3 years ago