Need Help with Limits? Let's Tackle These Questions Together!

In summary, the conversation is about someone seeking help with four questions they have been assigned. They have included scanned images of the questions and are not looking for direct answers but rather guidance to understand the concepts. The questions involve rationalization of the numerator and proving a given hint using induction. The person receiving help feels that the solutions provided so far are correct and is wondering about the limit of one of the questions.
  • #1
Mattofix
138
0
Limits - Please Help!

I have been set 4 questions, i basically have no idea if the ones i have tried are correct and have no idea how to even start the other 2. Any help would be much appreciated. I have scanned them in (easier than typing i think).

http://img90.imageshack.us/img90/7247/scan0001dg1.th.jpg [Broken] http://img230.imageshack.us/img230/562/scan0002ql7.th.jpg [Broken]I am not asking for the answers just some help to put me on the right path.

Thanks
 
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  • #2
b)use the rationalization of the numerator.
[tex] n \left( { \sqrt{1+n^{2}}-n } \right) = \frac{n \left( { 1+n^{2}-n^{2} } \right)}{\sqrt{1+n^{2}}+n} [/tex]
c)watch the given hint carefully!
[tex] \left( { \frac{3}{2} } \right)^{2n} < \left( { \frac{2n+1}{n+1} } \right)^{2n} [/tex]
you'd better prove the given hint by the induction...

I think the other answers are right in the way you solved.
 
  • #3
thats great, youv been really helpfull, one thing though.. does that mean c) lim xn tends to infinity?
 
  • #4
...
 

1. What is the concept of "Stuck on Limits Questions"?

"Stuck on Limits Questions" refer to mathematical problems or equations that involve limits, which are a fundamental concept in calculus. These types of questions often require students to evaluate the limit of a function as a variable approaches a certain value.

2. Why are "Stuck on Limits Questions" important in science?

Limits are crucial in many areas of science, including physics, engineering, and economics. They allow us to understand the behavior of a function or system as it approaches a certain value, which is important in making predictions and analyzing real-world phenomena.

3. How can I improve my skills in solving "Stuck on Limits Questions"?

Practice is key when it comes to mastering any concept in science. Start by understanding the basic principles of limits and then work on solving a variety of problems. Additionally, seeking help from a teacher or tutor can also be beneficial.

4. What are some common mistakes students make when solving "Stuck on Limits Questions"?

One common mistake is not understanding the difference between a limit and the actual value of a function. Another is not properly using algebraic techniques, such as factoring, when evaluating limits. It's important to carefully read and understand the problem before attempting to solve it.

5. How are "Stuck on Limits Questions" used in real-life applications?

Limits are used in many real-life applications, such as calculating the speed of an object at a specific time or determining the maximum or minimum value of a function. They are also used in modeling and predicting natural phenomena, such as population growth or the spread of diseases.

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