Help me please with some limits :D

Orimusa

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Hello everyone ! Can someone give me a solution with explanation if possible or just ideas :D thank you
The "[x]" sign is for Floor function
 

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Hello everyone ! Can someone please give me some solutions with explanations if possible or just ideas ^^ thank you
 
Hm... your image is a bit unclear to me. Is the first problem meant to be:

\(\displaystyle \displaystyle \frac{\lim _{x\to \infty }\left(\sqrt{9x^2+x-2}-\sqrt{25x^2-x+3}+2x\right)}{\lim _{x\to \infty }\left(\sqrt{11x^2-E\left(2x^2+x\right)}+3x\right)}\)

Or is the slash sign in the image just meant to indicate that these are two separate problems? Additionally, what is E in this context? Is it the same as e, or Euler's number? That is, is it meant to be a variable, or have the constant value 2.71828182845...?
 
Hm... your image is a bit unclear to me. Is the first problem meant to be:

\(\displaystyle \displaystyle \frac{\lim _{x\to \infty }\left(\sqrt{9x^2+x-2}-\sqrt{25x^2-x+3}+2x\right)}{\lim _{x\to \infty }\left(\sqrt{11x^2-E\left(2x^2+x\right)}+3x\right)}\)

Or is the slash sign in the image just meant to indicate that these are two separate problems? Additionally, what is E in this context? Is it the same as e, or Euler's number? That is, is it meant to be a variable, or have the constant value 2.71828182845...?

Oh no i am so sorry : the " / " sign is not meant to be for division. i used it to separate the limits. i shouldn't have used it. Replace it with " ; "
 
Hm... your image is a bit unclear to me. Is the first problem meant to be:

\(\displaystyle \displaystyle \frac{\lim _{x\to \infty }\left(\sqrt{9x^2+x-2}-\sqrt{25x^2-x+3}+2x\right)}{\lim _{x\to \infty }\left(\sqrt{11x^2-E\left(2x^2+x\right)}+3x\right)}\)

Or is the slash sign in the image just meant to indicate that these are two separate problems? Additionally, what is E in this context? Is it the same as e, or Euler's number? That is, is it meant to be a variable, or have the constant value 2.71828182845...?

I am sorry, i fixed the problems. The "/" sign is not for division, and the E is for Floor function : i changed the symbol.
 
Hello Everyone! i wish someone can help me with these limits. Solutions or ideas !

For number 2, i tried a lot to get rid of the indeterminate form ; i know that the only thing that makes a difference in what you are square rooting is the largest term. So basically, the first square root you see becomes 3x, the next is 5x.
But i got : lim 3x - 5x + 2x = lim 0x = 0 × ∞ (Indeterminate form)
 

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I am sorry, i fixed the problems. The "/" sign is not for division, and the E is for Floor function : i changed the symbol.

But where is your work towards solving the given "problems"??!!
 
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