Question

Limits again :)
  
   


     


    
 

 

Answer 1

\[ 1 - \frac{x^2}{4} \le \phi (x) \le 1 + \frac{x^2}{2}, ~~~~~\forall x \ne 0\\
~~\text{Calculate:}~~\lim_{x\rightarrow 0} \phi (x)\]
?

Answer 2

yeah

Answer 3

It looks like, as both the 'boundary' functions approach 0, we get 1 as the value. Since \( \phi (x) \) is between the two functions, it would have to approach that value as well. (So, squeeze theorem)

Answer 4

what access says. replace x by 0 on the left and on the right (since those functions are continuous, you compute the limit that way) and see that you get 1 on both sides

Answer 5

Thank you guys, helped a lot :))

Answer 6

You're welcome! :D