Homework Help Thread

[M. Bison]

Need a bit of a hand with -shudders- Calculus.

Basically, I need to work out:

lim(n -> ∞) of n+1- √(n^2 – n+1)

We actually haven't done finding limits yet, so this is actually a bit of extension... I still know what a limit is though, but if you use any special theora, you'll need to explain them...

You will first need to multiply and divide by the conjugate, that is:

lim (n+1- √(n^2 – n+1)) * [(n+1 + √(n^2 – n+1)) / (n+1 + √(n^2 – n+1))]

Note we are essentially multiplying the limit by 1, so we are not actually changing anything. If you distribute it out you get:

lim [(n+1)^2 - (n^2 - n + 1)] / [n+1 + √(n^2 – n+1)]

If you distribute out the top further, you can cancel the n^2 terms, and this gives you:

lim (2n + 1 + n - 1)/(n+1 + √(n^2 – n+1))

The numerator simplifies further and you get:

lim (3n)/(n+1 + √(n^2 – n+1))

Now we need to use a theorem known as L'Hopital's Rule. It states:

If lim f(x)/g(x) yields infinity/infinity or 0/0 upon substitution,
Then lim f(x)/g(x) = lim f'(x)/g'(x). Meaning you can take the derivative of the numerator and divide by the derivative of the denominator and the answer remains unchanged.

Note for us, lim n->infinity of (3n)/(n+1 + √(n^2 – n+1)) = infinity/infinity, thus:

lim (3n)/(n+1 + √(n^2 – n+1)) = lim (3n)'/(n+1 + √(n^2 – n+1))'

I rather dislike using this approach, because if you haven't done limits, I don't think you would have done derivatives yet either. But this is the only way I can think of to solve this limit without using even more complicated theorems (e.g. Taylor expansion). There might be some algebraic trick that I'm not seeing after we multiply by the conjugate. Maybe someone else can spot it.

Anyways, if you do take the derivative you'll get:

lim 3/(1 + (2n-1)^(-1/2)) = 3/[1 + 1/sqrt(2n-1)] = 3/(1+0) = 3

[Matt]

I rather dislike using this approach, because if you haven't done limits, I don't think you would have done derivatives yet either.

Yeah, we have. The British Maths syllabus actually teaches us the process of Differentiation and Integration first, followed by applications. The next two modules proceed basically to extend them e.g. teaching limits and partial fractions etc. This is basically an acceleration task, though I think this may have been a slightly clunky method of doing the task, I think it's probably the best one.

Anyways, cheers for your help. It's beddy-byes now but I'll have a look through that tomorrow

[guy679]

What's a suffix,prefix,diagraph, and a blend?
Help it's for my home work it's due tomorrow!

[Xil]

What's a suffix,prefix,diagraph, and a blend?
Help it's for my home work it's due tomorrow!

Wow, in what context? I'm assumming this is some sort of vocab work:

Suffix - An affix ended to the end of a root/stem word, functioning as a inflecting ending (hence changing the word)

Prefix - An affix attached to the front of a word to produce an inflected form (OR a derivative of the root/stem).

Diagraph - A tool combining a protractor and scale, often used for drawing to scale.

Blend - To combine various things to obtain a uniform mixture of a particular character, quality, or consistency.

[843]

I've got two Maths question here:
http://img384.imageshack.us/img384/4481/question9qb.jpg

EDIT: Here's another one. y is directly proportional to x^2. If x is increased by 100%, how many percent would y increase?

[fzun]

Ok I need a ton of help with my biology homework. I totally don't get this at all. And I unintentionally waited until the last second to get help from you guys so I need this by tomorrow morning and if you do help me I will love you forever and ever

6. A large amount of ATP in a cell inhibits the enzymes that catalyze the first few steps of glycolysis. How will this inhibition eventually affect the amount of ATP in the cell? Explain your answer.

2. How is the synthesis of ATP in the electron transport chain of mitochondria similar to the synthesis of ATP in chloroplasts?

5. What determines whether pyruvic acid will undergo lactic acid fermentation or alcoholic fermentation?

15. Most of the ATP synthesized in aerobic respiration is made (a) during glycolysis (b) through fermentation (c) in the cytosol (d) through chemiosmosis

20. How does aerobic respiration ultimately depend on photosynthesis?

21. Explain why some organisms produce lactic acid from pyruvic acid under anaerobic conditions, while other organisms produce ethyl alcohol

2. How does the folding of the inner mitochondrial membrane benefit aerobic respiration?

3. Yeast can produce ATP through either fermentation or aerobic respiration, depending on whether oxygen is present. If oxygen is present, yeast cells consume glucose much more slowly than if oxygen is absent. How can you explain this observation?

I've tried looking up the answers, this book is no help at all and I'm at a loss for what the answers are. So if you can help I would seriously love you forever [/quote]

[Shadow]

Answers are in red, hope I helped you.

6. A large amount of ATP in a cell inhibits the enzymes that catalyze the first few steps of glycolysis. How will this inhibition eventually affect the amount of ATP in the cell? Explain your answer.

I don't know

2. How is the synthesis of ATP in the electron transport chain of mitochondria similar to the synthesis of ATP in chloroplasts?

I believe it is because they both create a lot of ATP

5. What determines whether pyruvic acid will undergo lactic acid fermentation or alcoholic fermentation?

Well lactic acid fermentation is in the muscles and alcoholic fermentation is in yeasts so I'd think the answer is where it is located.

15. Most of the ATP synthesized in aerobic respiration is made (a) during glycolysis (b) through fermentation (c) in the cytosol (d) through chemiosmosis

I believe its C. but It could be D. I'm not entirely sure on this one

20. How does aerobic respiration ultimately depend on photosynthesis?

It needs the products of photosynthesis (oxygen and glucose) to go through respiration. Photosynthesis needs what respiration produces.

21. Explain why some organisms produce lactic acid from pyruvic acid under anaerobic conditions, while other organisms produce ethyl alcohol

I don't know

2. How does the folding of the inner mitochondrial membrane benefit aerobic respiration?

3. Yeast can produce ATP through either fermentation or aerobic respiration, depending on whether oxygen is present. If oxygen is present, yeast cells consume glucose much more slowly than if oxygen is absent. How can you explain this observation?

I don't know this either

I've tried looking up the answers, this book is no help at all and I'm at a loss for what the answers are. So if you can help I would seriously love you forever

[shapu]

Ok I need a ton of help with my biology homework. I totally don't get this at all. And I unintentionally waited until the last second to get help from you guys so I need this by tomorrow morning and if you do help me I will love you forever and ever

6. A large amount of ATP in a cell inhibits the enzymes that catalyze the first few steps of glycolysis. How will this inhibition eventually affect the amount of ATP in the cell? Explain your answer.

2. How is the synthesis of ATP in the electron transport chain of mitochondria similar to the synthesis of ATP in chloroplasts?

5. What determines whether pyruvic acid will undergo lactic acid fermentation or alcoholic fermentation?

15. Most of the ATP synthesized in aerobic respiration is made (a) during glycolysis (b) through fermentation (c) in the cytosol (d) through chemiosmosis

20. How does aerobic respiration ultimately depend on photosynthesis?

21. Explain why some organisms produce lactic acid from pyruvic acid under anaerobic conditions, while other organisms produce ethyl alcohol

2. How does the folding of the inner mitochondrial membrane benefit aerobic respiration?

3. Yeast can produce ATP through either fermentation or aerobic respiration, depending on whether oxygen is present. If oxygen is present, yeast cells consume glucose much more slowly than if oxygen is absent. How can you explain this observation?

I've tried looking up the answers, this book is no help at all and I'm at a loss for what the answers are. So if you can help I would seriously love you forever

[/quote]

Wow, that's actually a lot of hard questions.

6. By creating a negative feedback loop, the ATP/glycolysis interaction creates a limit of ATP density in the cell. (units per volume units). Too much ATP=too much activity=bad.

2. I dunno. I used to, but I forget. I suggest gooooooogle.

5. The first thing to remember is that lactic acid fermentation is basically (though not identically because of different situations) the same as glycolysis. So, basically, lactic acid fermentation occurs in bacteria, whereas alcoholic fermentation (which creates ethanol) occurs in yeasts.

15. Chemiosmosis is how ATP is produced by the mitochondrion. Is answer question?

20. Photosynthesis creates oxygen as a waste product. Build from there.

21. See five.

2 (number 2). increased surface area = increased area for electron transport to occur.

3. Aerobic respiration is a much more efficient way to use oxygen to create ATP than alcoholic fermentation is. So the cell can get the same amount of energy from less oxygen.

[guy679]

What's a suffix,prefix,diagraph, and a blend?
Help it's for my home work it's due tomorrow!

Wow, in what context? I'm assumming this is some sort of vocab work:

Suffix - An affix ended to the end of a root/stem word, functioning as a inflecting ending (hence changing the word)

Prefix - An affix attached to the front of a word to produce an inflected form (OR a derivative of the root/stem).

Diagraph - A tool combining a protractor and scale, often used for drawing to scale.

Blend - To combine various things to obtain a uniform mixture of a particular character, quality, or consistency.

Oh thanks!
I got it done in time!
(barely)

[fzun]

Lost + Shapu. I love you guys. Like you don't even know XD. I understand now, those questions just kinda went over my head .

[Ammer]

Need some help with Calc,

4. Find the extreme values of each function on the given interval, using the algorithm for maximum or minimum values.

a) f(x) = x + 4/x, 1 < x < 10

I was looking at my lesson and I started to derive the equation,

f(x) = x + 4x^-1
f'(x) = 1 -4x^-2

And I can't seem to factor it (Although, I'm almost positive I screwed up the deriving part). Can anyone help me?

[843]

Unless I'm mistaken, I think you just need to substitute f'(x)=0, since the maximum and minimum values are the turning points, where the derivation/gradient equals 0

1-4x^2=0
4x^2=1
x^2=1/4
x=+/- 1/2

I believe -1/2 is rejected since the interval is 1<x<10, leaving 1/2 as the only possible answer

[Ammer]

Unless I'm mistaken, I think you just need to substitute f'(x)=0, since the maximum and minimum values are the turning points, where the derivation/gradient equals 0

1-4x^2=0
4x^2=1
x^2=1/4
x=+/- 1/2

I believe -1/2 is rejected since the interval is 1<x<10, leaving 1/2 as the only possible answer

Sorry for replying so late. I thought I replied but it turned out I didn't, so, here I am. Anyways, that answer is right. Thanks for your help!

[fzun]

Ok, I need help with my biology homework again XD. I cannot wait until next semester when I won't have this anymore.

Cellular reproduction is the topic this time. (Ignore the weird numbering)

3. Compare the structure of prokaryotic chromosomes and eurokaryotic chromosomes.

My book fails to tell us x_x.

6. What would happen if cytokinesis took place before mitosis?

1. List two ways that meiosis differs from mitosis.

My book goes into their similarities more than their differences so it's difficult to find an answer.

6. Eplain why the chromosomes in the haploid cells that are produced by meiosis I look different from those produced by meiosis II.

20. Do asexual organisms have homologous chromosomes? Explain your answer.

22. Which of the following cells have a diploid number of chromosomes? Explain your answer.
(a) cells in the G1 phase of the cell cycle
(b) cells in the G2 phase of the cell cycle
(c) cells in the M phase of the cell cycle

1. Can mitosis occur in a cell in the absence of cytokinesis? Support your answer. If your answe ri syes, provide a description of how the new cell would appear in the G1 phase of the cell cycle.

5. For a cell to function efficiently, the magnitude of its surface area must greatly exceed that of its volume. Explain how cell division functions to maintain this relationshiop between surface area and volume and in doing so mantains cell homeostasis.

6. The events of mitosis in plans and animals are very similar with the exception of the absence of centrioles in plants. How has the absence of centrioles in plant cells influenced scientists' thinking about the function of centrioles in mitosis?

As usual, any help would be greatly appreciated and I would love you forever

[Squid]

Hey.

Ok, I need help with my biology homework again XD. I cannot wait until next semester when I won't have this anymore.

Cellular reproduction is the topic this time. (Ignore the weird numbering)

3. Compare the structure of prokaryotic chromosomes and eurokaryotic chromosomes.

My book fails to tell us x_x.

Prokaryotes have no nucleus, whereas eukaryotes, of course, do.

6. What would happen if cytokinesis took place before mitosis?

The cell would probably split, but only one would have a nucleus, resulting in a polar body. I'm not too sure about this one though.

1. List two ways that meiosis differs from mitosis.

Mitosis creates two daughter cells, whereas meiosis creates four. Mitosis creates two cells of the same genetic makeup, but meiosis creates cells with slightly different genetic makeup.

6. Eplain why the chromosomes in the haploid cells that are produced by meiosis I look different from those produced by meiosis II.

Meiosis I divides one diploid cell into two haploid cells by separation of homologous chromosomes, but meiosis II divides two haploid cells into four haploid cells by separation of sister chromatids.

20. Do asexual organisms have homologous chromosomes? Explain your answer.

Not sure about this.

22. Which of the following cells have a diploid number of chromosomes? Explain your answer.
(a) cells in the G1 phase of the cell cycle
(b) cells in the G2 phase of the cell cycle
(c) cells in the M phase of the cell cycle

(a) Diploid. This is a time of major growth.
(b) Diploid. The cell is preparing itself for the M phase.
(c) Yes and no. The cell is diploid at some point in mitosis, but the chromosomes split and are divided into two cell.

1. Can mitosis occur in a cell in the absence of cytokinesis? Support your answer. If your answer is yes, provide a description of how the new cell would appear in the G1 phase of the cell cycle.

See the second question up there. It's basically the same.

5. For a cell to function efficiently, the magnitude of its surface area must greatly exceed that of its volume. Explain how cell division functions to maintain this relationshiop between surface area and volume and in doing so mantains cell homeostasis.

I think this is like telophase, but I'm not sure.

6. The events of mitosis in plans and animals are very similar with the exception of the absence of centrioles in plants. How has the absence of centrioles in plant cells influenced scientists' thinking about the function of centrioles in mitosis?

Scientists believe that centrioles may help organize microtubule assembly, but they are not essential to formation of the mitotic spindle.

As usual, any help would be greatly appreciated and I would love you forever

Love me forever.