Jackson has a credit card with a 15% interest rate. His dad has a credit card with a 5% interest rate. If they both charge $1,00
2 answers:
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To demonstrate a method for computing the limit itself, let's pick a small value of n. If n = 3, then our limit is
Let a = 1 and b the cosine product, and write them as
with
Now we use the identity
to rationalize the numerator. This gives
As x approaches 0, both a and b approach 1, so the polynomial in a and b in the denominator approaches 6, and our original limit reduces to
For the remaining limit, use the Taylor expansion for cos(x) :
where essentially means that all the other terms in the expansion grow as quickly as or faster than x⁴; in other words, the expansion behaves asymptotically like x⁴. As x approaches 0, all these terms go to 0 as well.
Then
so in our limit, the constant terms cancel, and the asymptotic terms go to 0, and we end up with
Unfortunately, this doesn't agree with the limit we want, so n ≠ 3. But you can try applying this method for larger n, or computing a more general result.
Edit: some scratch work suggests the limit is 10 for n = 6.
Answer:
Required center of mass
Step-by-step explanation:
Given semcircles are,
whose radious are 1 and 4 respectively.
To find center of mass, , let density at any point is
and distance from the origin is r be such that,
where k is a constant.
Mass of the lamina=m= where A is the total region and D is curves.
then,
- Now, x-coordinate of center of mass is
. in polar coordinate
Then,
- y-coordinate of center of mass is
. in polar coordinate
Then,
Hence center of mass
Answer:
Graph One.
Step-by-step explanation:
See below. The graph is in a straight line, also known as linear. The other graphs are not. Also, if you look at the range (y) of the tables, you can see the increase is linear as it is increasing by .5 (1/2) everytime.
