Tuesday, April 22, 2008

This is for Mrs. Carlson:
When using p-series or harmonic series, do you have to equate it to DCT or LCT or can you just write the similiar equation and the formula?

For instance, woudl 1/n, diverges, harmonic series, be acceptable or do we have to equate the similiar equation to the orignial equation through DCT or LCT?

Onto the HW:

6b. The answer integrated it and as the limit approached infinity, it was heading towards infinity. Why, then does it diverge? It's not using the nth term test, is it?

9b. Since f''(x) is less than zero, does this mean that there is a relative max as x=2?

13c. I don't get the significance of the integral's limits being at x=z and x=0. There doesn't seem to be any difference.

14a. When testing endpoints at x=-1 and x=1, the resuult tends to be the same. So why the function diverges at x=-1 and vice versa at x=1 leaves me puzzled.

15b. a= -3(1/4) and it looks like r=1/4. But the answer would equal to -1 then and that wouldn't make sense.
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1 comment:

MariaCJen said...

for 6b, i think because it is approaching infinity as the limit approached infinity, its limit does not exist, which according to the Nth term test means that it will diverge

for 9b, on page 200 in our math book it states that if f'(c)=0,
and f''(c)<0, then there is a local max. at x=c;
and f''(c)>0, then there is a local min. at x=c;
that should help

for 13c, i think it's because you are integrating f(t)dt and you need it to be in terms of x. i'm not 100% sure so sorry if i am wrong

for 14a, i got that the function diverges for both x=1 (alt. series) and x=-1 (Nth term), so i didn't include both endpoints in my IOC

for 15b, this took me a really long time, but i found that the series in part a is equal to f'(1/2).. if you look at the nth term in part b and plug in 1/2 to it and the derivative of the nth term of part a you will see that they are the same. then i found what f'(x) was using the equation they give you in the beginning and then i just plugged in 1/2 to f(x) sorry if this is confusing. this is how i did it and i got the right answer eventually so im guessing that it's right

April 23, 2008 at 8:35 PM

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