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

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Homework Help Overview

The discussion revolves around evaluating limits, specifically focusing on two problems: the limit of (sin(√(1-x)))/√(1-x²) as x approaches 1 from the left, and the limit of (x² + sin(x))/(x² + cos(x)) as x approaches infinity.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of L'Hopital's rule for the first limit and discuss the bounded nature of sine and cosine functions compared to the unbounded nature of x². Questions arise regarding the clarity of the original expression and the interpretation of x² versus 2*x.

Discussion Status

Some participants have provided insights and attempted to clarify the expressions involved. There is an ongoing exploration of the first limit, while one participant has successfully evaluated the second limit, indicating a productive direction in the discussion.

Contextual Notes

Participants note the original poster's struggle with the problems due to a heavy workload and the approaching deadline for their assignment. There is also a mention of potential confusion regarding the notation used in the limit expressions.

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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
 
Last edited:
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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?
 
Last edited:
ok i fixed the parentheses,

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

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