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3 years ago

I don't know how do this, I know that I use L'hopitals Rule, I just don't know who to start.

1 answer:

5 0

Lim[x.sin(4π/x)] when x →∞. To apply the Hospital rule we need a fraction:

lim[x.sin(4π/x)] could be written:

lim [sin(4π/x)] / (1/x) . Now let's find the derivative of the numerator and the denominator:

Numerator = sin(4π/x) → (Numerator)' = cos(4π/x).(-4π/x²) [Chaine rule
(sinu)' = cosu. u'] So derivative of Numerator = cos(4π/x).(-4π/x²)

Denominator = 1/x → Numerator derivative = -1/x²

Now : (numerator)'/(denominator)' = cos(4π/x).(-4π/x²) / -1/x²
Simplify by x² : → cos(4π/x).(-4π) / -1

OR cos(4π/x).(4π) . When x→∞ , 4π/x → 0 and cos(0) = 1, then:

lim[x.sin(4π/x)] when x →∞. is 4π

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Rufina [12.5K]

Answer:

$84 {x}^{12} \:$

Option C

Step-by-step explanation:

$(4x)( - 3 {x}^{8} )( - 7 {x}^{3} )$

$(4x)(21 {x}^{8 + 3} )$

$84 {x}^{1 + 11}$

$84 {x}^{12}$

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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-1/2(3x-4)+3x=5/6 Please help

Ksenya-84 [330]

Answer:

x = -7/9

Step-by-step explanation:

The usual recommendation is to clear fractions first. Here, you can do that by multiplying both sides of the equation by 6.

6(-1/2(3x -4) +3x) = 6(5/6)

-9x +12 +18x = 5 . . . . . . . . . simplify

9x = -7 . . . . . . . . . . . . . . . . . subtract 12

x = -7/9 . . . . . .divide by 9

Another way to do this is to eliminate parentheses first.

-3/2x +2 +3x = 5/6

3/2x = -7/6 . . . . . . . . . collect terms, subtract 2

x = (-7/6)(2/3) = -7/9 . . . . multiply by 2/3

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3 years ago

Which intervals are most appropriate for a histogram

Lorico [155]

Answer:

C. 10–15, 15–20, 20–25, 25–30, 30–35

Step-by-step explanation:

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3 years ago

The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

BartSMP [9]

Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

$c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm$

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

$\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} = \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm$

$r = 8.9 \pm 0.2 cm$

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

$A=\pi r^{2}\\A=249 cm^{2}$

Then we calculate the error:

$\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}$

$A=249 \pm 11.2 cm^{2}$

Now we proceed to calculate the percent error:

$\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%$

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

$\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}$

Now we calculate the error for the radius:

$\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm$

Now we proceed with the error for the circumference:

$\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm$

5 0

4 years ago