Calculus I ..DESPERATELY NEED HELP

[qwerty1]

I am not able to solve some questions so I decided to post them on yahoo answers. I got answers to some of them and I just want you to check them.

But some others I don't understand at all.

 

NOTE : PLEASE DO THE QUESTIONS ONLY IF YOU ARE 100% SURE

 

Here are the questions.

 

#1 - #5 ** ANSWER PROVIDED CHECK IT PLEASE **

 

1)

Suppose that x^2-6x-3 <= f(x) <= sqrt(9-x^2) on

[0,3]. Give upper and lower bounds for lim x->0+ f(x) and lim x->3^- f(x)

 

lim (x^2 - 6x - 3) = -3 as x --> 0+

lim sqrt(9 - x^2) = 3 as x -->0+

 

-3 = f(x) = 3

 

lim (x^2 - 6x - 3) = -12 as x --> 3-

lim sqrt(9 - x^2) --> 0 as x --> 3-

 

-12 = f(x) = 0

 

(What is the upper bound and lower bound ? I don't know that.)

 

2)

Does there exist a real number that is exactly one more than its own square root? Justify your answer (hint: intermediate value theorem)

 

x = (sqrt(x)) + 1?

 

f(x) = x - (sqrt x) - 1 > 0?

f(0) = -1

f(4) = 1

 

There is a value a between 0 and 4, where a = (sqrt a) + 1.

Namely, a ˜ 2.618.

 

3)

True or False: if f is continuous at c, then 1/f is continuous at c. Justify your answer with a proof or counterexample.

 

If the lim exists for f at c, then the lim exists for 1/f at c also.

 

(I know the sentence but needed a counter example.)

 

4)

Where is the function

f(x) = | ln(x)+(sin(e^x)/x^2+5) |

defined, and where is it continuous ?

 

f(x) is defined for all x > 0, and is continuous on its domain.

 

(I know the sentence but needed an example.)

 

5)

Determine where the function f(x) = (x^2+5x+6)/(x+3) is discontinuous, and define a continuous extension g of f.

 

I know the function f(x) is discontinuous at x = -2, but I don't know how to define a continuous extension g of f.

 

6) Evaluate

go to this link to see the function because it is confusing if i write it out. The "input" is the function.

 

http://tinyurl.com/3uutnv5

-------------------------------------

There are two more graph questions

 

1) Sketch the graph of a function f that satisfies all the following conditions:

 

f(0) = 1

f(-1)= -2

lim x->0 f(x) = inf

lim x->inf f(x) = 0

lim x-> -inf f(x) = 2

lim x-> -1^+ f(x) = 3

lim x-> -1^- f(x) = 1

 

I have the graph on the following link. Check it and tell me what is wrong.

 

http://tinyurl.com/3mzb7fb

 

2) Sketch the graph of a function that has vertical asymptotes at x = -3 and x = 2, horizontal asymptotes at y = 1 and y = 0, and domain (-inf,-3) U (-3,inf)

 

( I have no idea about this one)

 

-------------------------------------

 

I appreciate the help a lot. THANKS

 

I am not able to solve some questions so I decided to post them on yahoo answers. I got answers to some of them and I just want you to check them.

But some others I don't understand at all.

 

NOTE : PLEASE DO THE QUESTIONS ONLY IF YOU ARE 100% SURE

 

Here are the questions.

 

#1 - #5 ** ANSWER PROVIDED CHECK IT PLEASE **

 

1)

Suppose that x^2-6x-3 <= f(x) <= sqrt(9-x^2) on

[0,3]. Give upper and lower bounds for lim x->0+ f(x) and lim x->3^- f(x)

 

lim (x^2 - 6x - 3) = -3 as x --> 0+

lim sqrt(9 - x^2) = 3 as x -->0+

 

-3 = f(x) = 3

 

lim (x^2 - 6x - 3) = -12 as x --> 3-

lim sqrt(9 - x^2) --> 0 as x --> 3-

 

-12 = f(x) = 0

 

(What is the upper bound and lower bound ? I don't know that.)

 

2)

Does there exist a real number that is exactly one more than its own square root? Justify your answer (hint: intermediate value theorem)

 

x = (sqrt(x)) + 1?

 

f(x) = x - (sqrt x) - 1 > 0?

f(0) = -1

f(4) = 1

 

There is a value a between 0 and 4, where a = (sqrt a) + 1.

Namely, a ˜ 2.618.

 

3)

True or False: if f is continuous at c, then 1/f is continuous at c. Justify your answer with a proof or counterexample.

 

If the lim exists for f at c, then the lim exists for 1/f at c also.

 

(I know the sentence but needed a counter example.)

 

4)

Where is the function

f(x) = | ln(x)+(sin(e^x)/x^2+5) |

defined, and where is it continuous ?

 

f(x) is defined for all x > 0, and is continuous on its domain.

 

(I know the sentence but needed an example.)

 

5)

Determine where the function f(x) = (x^2+5x+6)/(x+3) is discontinuous, and define a continuous extension g of f.

 

I know the function f(x) is discontinuous at x = -2, but I don't know how to define a continuous extension g of f.

 

6) Evaluate

go to this link to see the function because it is confusing if i write it out. The "input" is the function.

 

http://tinyurl.com/3uutnv5

-------------------------------------

There are two more graph questions

 

1) Sketch the graph of a function f that satisfies all the following conditions:

 

f(0) = 1

f(-1)= -2

lim x->0 f(x) = inf

lim x->inf f(x) = 0

lim x-> -inf f(x) = 2

lim x-> -1^+ f(x) = 3

lim x-> -1^- f(x) = 1

 

I have the graph on the following link. Check it and tell me what is wrong.

 

http://tinyurl.com/3mzb7fb

 

2) Sketch the graph of a function that has vertical asymptotes at x = -3 and x = 2, horizontal asymptotes at y = 1 and y = 0, and domain (-inf,-3) U (-3,inf)

 

( I have no idea about this one)

 

-------------------------------------

 

I appreciate the help a lot. THANKS

 

 

Omg !! No one wants to help...I am the only person to whom no one has replied. When I really need help no one is gonna help.

ughhh .. i am gonna fail this thing.

Edited October 10, 2011 by qwerty1

[mooeypoo]

You got help in the IRC channel, qwerty1, calm down. You posted this TONIGHT, and people aren't here 24 hours a day. This is why you shouldn't delay homework for the last moment, or come to a forum of volunteers and demand we drop everything and help you out.

 

 

That said, I'm finding it hard to see what exactly you're asking. In the first question you wrote

 

"Give upper and lower bounds for lim x->0+ f(x) and lim x->3^- f(x)" So it seems the 'upper and lower bounds' are stated as x from 0 to infinity. Is that what you're asking?

 

Question 4 is also unclear..

 

 

4)Where is the function

f(x) = | ln(x)+(sin(e^x)/x^2+5) |

defined, and where is it continuous ?

 

f(x) is defined for all x > 0, and is continuous on its domain.

 

(I know the sentence but needed an example.)

I don't understand -- you're giving us a question with an answer and then ask for clarification? Is this answer your answer or is it someone else's that you're trying to understand why they answered the way they have? Do you know how to check for continuity at all or is this just a specific question regarding ln and sin?

 

We're not here to feed you answers, we are here to help you answer the questions. I will need a bit of help from you to know how to start helping you out.

 

~mooey

[csmyth3025]

I can't help you because I'm trying, myself, to learn math at the very level that your problems illustrate.

 

I definitely agree with Mooeypoo. Your original post is time-stamped at 7:43 pm today and your "...Omg !! No one wants to help...I am the only person to whom no one has replied..." is time stamped two minutes later at 7:45 pm. Your expectations for a response are unrealistic (to say the least).

 

It's my understanding that this section will provide you with pointers to help you figure out the correct answers to homework problems. Your opening statement makes this a bit problematic, though:

 

I am not able to solve some questions so I decided to post them on yahoo answers. I got answers to some of them and I just want you to check them.

But some others I don't understand at all...

 

It seems that the answers that you have provided in your post are not your own, but, rather, someone else's answers. You don't seem to understand how these answers were derived and, in some cases, you don't seem to understand what they mean.

 

I'm sure that you can find assistance here that will help you figure out how to solve these problems. I'm not sure that anyone here will verify an answer that someone else has given you or provide you with an answer to one of your problems.

 

Chris

[mooeypoo]

qwerty, you need to, at the very least, TRY. If you give us a bit more of your OWN steps to the questions (what did you try? what do you think should be the beginning, etc) we can help. Otherwise, we can't really start teaching calculus from scratch without a direction of where to go with it.

[DrRocket]

qwerty, you need to, at the very least, TRY. If you give us a bit more of your OWN steps to the questions (what did you try? what do you think should be the beginning, etc) we can help. Otherwise, we can't really start teaching calculus from scratch without a direction of where to go with it.

 

The problem with the stated urgency is that it makes it quite clear that the OP is responsible for turning in or presenting the solutions to these problems very soon, probably tomorrow.

 

Moreover the nature of the questions is that of a set made up to test a relatively broad set of concepts. It is much too broad to be a set of simple homework exercises for a single section of a textbook or set of lecture notes.

 

That makes this not really homework, but more like a take-home test. It clearly carries credit.

 

When I took calculus, and when I taught calculus, the use of help such as is being sought here would have been considered blatant cheating.

 

These problems are not all that hard, but they do take a bit of thought -- rote application of cookbook calculation methods won't do. This makes it more disturbing that the OP has shown zero work of his own and is asking for solutions.

 

I am not inclined to abet cheating.

[mooeypoo]

The problem with the stated urgency is that it makes it quite clear that the OP is responsible for turning in or presenting the solutions to these problems very soon, probably tomorrow.

 

Moreover the nature of the questions is that of a set made up to test a relatively broad set of concepts. It is much too broad to be a set of simple homework exercises for a single section of a textbook or set of lecture notes.

 

That makes this not really homework, but more like a take-home test. It clearly carries credit.

 

When I took calculus, and when I taught calculus, the use of help such as is being sought here would have been considered blatant cheating.

 

These problems are not all that hard, but they do take a bit of thought -- rote application of cookbook calculation methods won't do. This makes it more disturbing that the OP has shown zero work of his own and is asking for solutions.

 

I am not inclined to abet cheating.

 

Which is why this forum has this policy of not giving out the answers with a spoon, and why I insisted he shows us, at least, what he is trying to do.

 

We can't know if something is a test or not or if people are cheating -- that, quite honestly, is the responsibility of the individual and the professor that chooses to trust them with a take-home exam. What we *can* do is try to make sure the poster cooperates and, at least, "gets" something out of it -- understands the material, sees where their problems are, or how to solve similar problems.

 

I tend to be suspicious when a poster posts multiple questions in a series as this one did, too... if you can't do ANY of the problems you were given for a homework assignment, there's a much much bigger problem here. I'm not too sure we can solve that, though.

 

~mooey

[mooeypoo]

Qwerty, you keep coming to the IRC channel, but you have to do your "homework" first.

 

Here are a few video lessons that can help you:

 

Limits: http://www.khanacademy.org/video/introduction-to-limits--hd?playlist=Calculus

Limit Example 1: http://www.khanacademy.org/video/limit-examples--part-1?playlist=Calculus

Limit Example 2: http://www.khanacademy.org/video/limit-examples--part-2?playlist=Calculus

Limit Example 3: http://www.khanacademy.org/video/limit-examples--part3?playlist=Calculus

 

Each one of those videos is about 7-8 minutes. They're short, but they're very informative. You have to know the basics before we can help you solve these questions, we're not going to start redefining and teaching the entire course from scratch.

 

Enjoy

 

~mooey

[baric]

I am not inclined to abet cheating.

 

After all, there is no indication the OP has done any work at all. His answers are from Yahoo Answers.

Edited October 12, 2011 by baric