Limit of a series

Does anyone know how to do problems like set 1 #43? I don't remember learning anything about finding the limit of an infinite series. Anyone know what to do?

Set #1

Let's get straight to the questions.

5. I'm not able to come to a conclusion from the info given
21. Do you differentiate the unction and if so, what comes next?
23. I got (1/h) [ (-e^(-1)/2+(1/2e)]
28. The functions looks more like a parabola than a sphere- I'm not sure how they arrived at a volume here.
30. I anti-differentiated it to (e^(1+lnx))/(1/x) and then came to 16e-4e=12e.
35. I differentiated [(1/2)y(3^.5/2)y] and got 36(3)^.5
36. I differentiated x^2-kx from 2k to zero and got k^3=54.
37.For f'(g(0)), I got 11, so it already isn't working out for me.
38. Using the arc formula, I came to [(35-4x^2)/(36-4x^2)]^.5, which I should differentiate from three to zero, although the answer seems unlikely.
43. I don't see the connection between the antiderivative of x^2 and the limit above
45. We're not allowed to use calculator, so I'm further perplexed as to what they're trying to find.

Thanks for your help.

#20 from Multiple Choice Set#1 - No calculators

Does anyone know how to explain this? I tried plotting points, but my graph doesn't come out as the same one that they give us.. what am I doing incorrectly?

#20

For part A...
How come the third term is (1/16) when even the solutions say 2!/4(4) ?
For part B...
Where does the (x-5) in the Ratio Test come from?

#4, Error Problems

I'm stuck on 4. I can't find what the general form of the derivative is, and I can't set up the general term of the power series, so I can't continue on with the problem. Also, does anyone how to solve the error problems like 4c. The solutions mentioned the alternating series test, but I don't think we ever learned how to estimate error with alternate series. Anyone know what to do?

Finding IOC

Hi guys! Is anyone here good at finding the IOC? I have difficult time with this subject so can someone please help me? For example: Infinites Series number 4. How would you know that the IOC is -0.6_< x _< 0.6? I am confuse.

Infinite Series Homework Help

Infinite Series is really difficult for me to understand...
Anyways I need help on #2-c and #4-c...
I know for number #4-c you use the Remainder Theorem but can someone help me understand how to use that please.
Thanks

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.

Infinite Series

Wow, what a confusing chapter

2b. The answer antidifferentiated it and added a "c." When integrating a series, do you always have to add a c? Also, I don't get how they got c to equal to -2, I mwan, I know they put ln(2-1)=0, but I don't understand why they did that.

4a. When you find f'(0) and f''(0)...I got -4xe^(-2x^2), 16xe^(2e^9-2x^2), so when you plug in the zero, f'(0)=0 and f''(o)=0, so apparently, the answer is just f(0) , since the other functions=0. What am I doing wrong?
b How do I know IOC if I don't have an r?
c.The answer put it at lf(x)-g(x)l is less than or greater than (16x^8)/4!. How did they know to stop at the 4th degree?

7a. I don't get how they found the equation to use to for finding the IOC.

9d. The LaGrange formula confuses me because I don't know to which degree I should use. In this case, they use it to the 4th degree.

10b. The LaGrange formula confuses me because I don't know to which degree I should use. Why is it the 4th degree in this case?

If you don't get what I'm asking, could you just show me what ways you used to solve the problem or what I may be doing incorrectly? Thanks.

#4c from HW #21

Can someone explain this question? Thanks.

HW 21

Does anyone know how to do 2c?
Thanks

#18 from HW #19

Does anyone know how to do this problem? I looked at the solutions and they used an integrating factor? Can someone explain this to me? Thank you.

Particle motion

6d. For 5c, the answer was simple- when is x=0? But how do you solve this question?
7 is really confusing for me because they don't explain where ABCD is located. For 7a, how do you know that dy/dy and dx/dt at C is increasing?

Also, which concepts we should review for the quiz, Mrs. Carlson?

quiz on friday

is it only based on this week's hw
or also spring break's?

Need help

This isn't good- I don't get a lot of the hw questions (Are there step by step answers for the sets?). In any case, let me point out a few that I have trouble on.

Set 1
18. I looked for A', which is .5(bh'+hb') and got .5(-20(.5)-15(1/3))
30. The answer is e but e doesn't satisfy the first requirement

Set 2
4. I don't get which formula I should use
15. After cross multiplying, I got y=2x
19 I have no idea how the nswer is a, besides the fact that there is an asymptote at y=10
31. Which formula did you use?
33. You l'hopital, I differentiated it to -8sin4x and -32cos4x and neither solution matches the answer
39. Don't quite get how they shaped the formula.
40. I differentiated it and got zero

Set 3
4. Which formula did you use?
7. Isn't is 3/4
9. I got -1/720

Thanks

HW#19 & #20

Does anyone know where I can find it to download? The Polar/Parametric problems? When I click the link on Edline it doesn't go to the file. Thanks!

#6b from HW #17

I got the speed but I can't find the acceleration vector. I thought to find the acceleration vector you just find the second derivative, or the derivative of dx/dt and dy/dt, but my answer isn't the same. Does anyone know how to find the acceleration vector? Thanks.

Number 10 from Set #3

Can anyone explain how to do this problem? Thanks!

Set 1

How would you do #2 and #29?
Can someone explain please?

Number 30 from Set#2

To find the volume do we find the area of the base and multiply it by 2 because that's the height? Because that's how I was doing it but the answer isn't any of the choices and then the answer key says the answer is D but I keep getting that the value of D is the value of the base. Am I doing something wrong?

Finding growth rate

I was wondering can someone explain to me how you find the growth rate when it gives you the differential equation (which models the growth)? Or do you remember the section that we learned this?

I'm sorta referring to problem #18 in second multiple choice set if you don't understand my question.

Thank you for any help!

MC sets

I was wondering if our homework is all of the sections of the MC packet. It says set 1 online, but does that mean only the first section on differentials?

MC set#1 answers

Hi Mrs. Carlson,
I think that one of the answers on set #1 is wrong. #30's answer says E but I don't think that is correct because the question says that the limit as x approaches 1+ is -inf. and choice E is not correct. I think the answer should be C. I would appreciate it if you could check it out.
Thank you.

MC Set #1

Limits, Differentiation, Applications of Derivatives:

#20: how do figure out the equation of the tangent line?
if g(x)=f^-1(x), then if f'(2)=3/4, would g'(-3)=-4/3?

#22: How do we use the Mean Value Theorem to find c? I know that c'=(f(b)-f(a))/(b-a), but how do you use that to find c?

HW #15: 18c

I know the hw packet is due tomorrow, but I just want to know how you find out that P is a local maximum. I looked at the solutions, but I still don't get it!
Have a great spring break everybody!

Hw #12+

#12
1d. I get how P'(o) =2, but why is t=5?
2a. How did it arrive at y=.5?
4a. What formula was used to find out the limit? Is it the sae used for 2a in #13?
4b.The answer states it occurs when the population is half of the carrying cpacity- how do you know that?

#13
2c. The range is just when f(x) is positive. Is f(x), then, only a function when it's positive? The same thing happens with 5b.

#14
1b. Strangely, when I do it, it's -(2+sinx)sinx-(cosx)^2=0, yet the answers say it's at sinx=.5. What am I missing?
9b. I don't get how they found the x and y intercepts.

Thanks for your help!

Test on Friday

I'm confused over which subjects we're going over- it seems like a mix of past topics. Can you tell us which chapters we should be paying more attention on? Because I'm looking up the topic that's stated on our hw, and the chapter index doesn't give many pages on it...

When they say "justify our answer," I'm stumped because when the hw answers justifies it, it's often in different ways. Is there one, consistent, formula for justifying your answer? Like:

The realtive max is at x=1 because f '(x) changes from postive to negative at tis value
The relative max is at x=1 because f (x) changes from decreasing to increasing at this value

Just making sure.