Mastering Limits: Tips for Solving Tricky X^2 Problems | Homework Help"

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In summary: I was trying to figure out the first one over hereIn summary, the first limit is equal to 1/root2 and the second limit is equal to 1. Both can be solved using L'Hopital's rule and factoring.
  • #1
skateza
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Homework Statement


lim as x approaches 1 from the left of (sin[tex](\sqrt{1-x})[/tex])/[tex]\sqrt{1-x2}[/tex]

and

lim as x approaches infinity [tex](x^{2}+sinx)/(x^{2}+cosx)[/tex]


The Attempt at a Solution


I have attempted to solve these although my brain is raw, i have done a hundred limits today because my assignment is due tomorrow and I am just lost on these ones... any starting tips
 
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  • #2
The second one is easy. sin and cos are bounded. x^2 isn't. Your first problem doesn't have enough parentheses in it to make it clear. But in any event, since it looks like it is of a 0/0 form I would use L'Hopital's rule. Is it sin of the whole thing or just of the first sqrt. And does x2 mean 2*x or x^2?
 
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  • #3
ok i fixed the parentheses,

What do u mean by sin and cos are bounded
 
  • #4
I mean |sin(x)|<=1 and same for cos while x^2 goes to infinity. Now does x2 mean x^2 or 2*x?
 
  • #5
sorry, yeah it means x^2
 
  • #6
I'm still going for trying to hit the first one with L'Hopital's rule. How's the second one going?
 
  • #7
Isn't the first one just sin x / x in disguise?
 
  • #8
Hurkyl said:
Isn't the first one just sin x / x in disguise?

Sure it could be done that way. I'm still waiting for the OP to do SOMETHING. The second one is not that hard.
 
  • #9
I've solved the second one, i got 1, easy... just divided by the highest power of x in the denom. I did it a while ago i just for got to post sorry haha... but the first one has still got me,, because their is an x^2 in the bottom, so its not quite sinx/x
 
  • #10
You can factor (1-x^2)=(1-x)*(1+x). I was wondering if I had lost you.
 
  • #11
perfect solved it, 1/root2
 
  • #12
Yes you did.
 

FAQ: Mastering Limits: Tips for Solving Tricky X^2 Problems | Homework Help"

1.

What are the key components of mastering limits in solving tricky x^2 problems?

The key components of mastering limits in solving tricky x^2 problems include understanding the concept of limits, knowing the properties of limits, understanding the different types of limits (including one-sided and infinite limits), and being familiar with the rules for solving limits (such as the limit laws and L'Hopital's rule).

2.

How can I improve my skills in solving tricky x^2 problems involving limits?

To improve your skills in solving tricky x^2 problems involving limits, it is important to practice regularly and work through a variety of problems. It can also be helpful to seek out additional resources, such as textbooks or online tutorials, to supplement your learning.

3.

What are some common mistakes to avoid when solving x^2 problems involving limits?

Some common mistakes to avoid when solving x^2 problems involving limits include forgetting to check for one-sided or infinite limits, incorrectly applying the limit laws or other rules, and not simplifying the expression enough before solving the limit.

4.

How can I determine when to use L'Hopital's rule in solving x^2 problems involving limits?

L'Hopital's rule is typically used when the limit involves an indeterminate form, such as 0/0 or ∞/∞. If you encounter an indeterminate form while solving a limit, you can try applying L'Hopital's rule to simplify the expression and continue solving the limit.

5.

Are there any other helpful tips for mastering limits in solving tricky x^2 problems?

Aside from regular practice and seeking additional resources, it can also be helpful to break down the problem into smaller steps and approach it systematically. It can also be beneficial to review and understand the concept of continuity, as it is closely related to limits and can aid in solving tricky x^2 problems.

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