Question

Ajuda please me ... é urgent ....

Answer 1

Notice that
\[\int_{-2}^{-1} \frac{1}{x^{2}} dx = \int_{-2}^{-1} x^{-2} dx\]
So we can just flip the power rule for derivatives around backwards and see that \[\int x^{n} dx = \frac{1}{n}x^{n+1}\] and thus our integral becomes \[\int_{-2}^{-1}x^{-2} dx = -x^{-1}|_{-2}^{-1} = \frac{-1}{x} |_{-2}^{-1} = 1 - \frac{1}{2} = \frac{1}{2}\]

Answer 2

Thank you my friend, very intelligent you .....

Answer 3

lol you're welcome. It's just practice. Most of mathematics is just a matter of recognizing how to put things into an easier form.

Answer 4

Okay, I really need your help with some exercises like this, if you can help me I would be very grateful .... you have facebook?

Answer 5

I don't, sadly. You can just message me here though, and I'm happy to help

Answer 6

Ok, when you need to send you a message here ... thanks friend ... I have to leave now ... a hug ...

Answer 7

Can you do this?

Answer 8

The demand for a certain brand of portable alarm function is given by:

p = - 0,01.x^2 - 0,3x + 10

Where p is the unit price at the wholesale real ex, the quantity demanded each month, measured in units of thousands. The bid for this watch brand function is given by:

p = - 0,01x^2 + 0,2x + 4

Having po same meaning as before and where x amount, in thousands, that the supplier will market monthly. Determine the consumer surplus and the surplus production when the unit market price is equal to the equilibrium price.

Answer 9

From what I understand, this is telling you that the supply curve is given by \[p_1 = -0.01x^{2} - 0.3x + 10\]and the demand curve, i.e. the bid that customers are willing to pay is given by \[p_2 = -0.01x^{2} + 0.2x + 4\]
I don't really understand the translation 100%, but it makes sense so far. Consumers will buy the watches when \[-0.01x^{2} - 0.3x + 10 = -0.01x^2 + 0.2x + 4\] Simplifying, we get \[-0.3x + 10 = 0.2x + 4\]\[-0.5x + 6 = 0\]\[-0.5x = -6\]\[x = 12\]
So our equilibrium price is $12 (or whatever currency--"$" is the only one I have on my keyboard.) Now the battle is half over, we just want to find out how many consumers aren't satisfied and how many watches won't get sold at the equilibrium price. First, we plug in x = 12 to our equation to get the quantity:
\[p_1(12) = -0.01(144) - 0.3(12) + 10 = 4.96\]and, if we want to check our math above, we can verify that we get the same answer for the other function:\[p_2(12) = -0.01(144) + 0.2(12) + 4 = 4.96\]
So our equilibrium price is $12, and our equilibrium quantity is 4.96 (times 1000) watches.

Our consumer surplus is the area below the demand curve, above the equilibrium price, and our producer surplus is the area above the supply curve, below the equilibrium price. At this point, it's going to be helpful to look at a graph, which will basically look like this:

All that's left to do is find the area above and below these curves, which is where calculus comes in. Your consumer surplus is going to be below the demand curve, but above y = 4.96. That means you're basically finding the integral of the demand function and subtracting a rectangle with dimensions 4.96x12 (or in general, x by f(x)), which is given by \[\bigg(\int_{0}^{12} -0.01x^{2} - 0.3x + 10\,dx\bigg) - 4.96*12\]
That's a pretty simple integral to solve, so I'll move on to the next area: above the supply curve, below y = 4.96. Integrals aren't generally that helpful in finding area above curves, but here you have an upper bound, so you can find it the opposite way from what you did previously, and find that your other surplus is given by
\[4.96 * 12 - \bigg(\int_0^{12} -0.01x^{2} + 0.2x + 4\,dx\bigg)\]

Hope that's enough!