The definition of a limit is  lim(x-->a)  = L    if:



        |f(x)-L| <    for  0 < |x-a| < 





So here,  = 1, centered at x=0, so we need to evaluate f(-1) and f(1): 

    f(-1) = 

    f(1) = 



So the exact value of  is  =   or approx. 0.2361



Here, the function is symmetrical about the limit point x=0.  If the function was not symmetrical, you'd evaluate f(x) on both sides of the limit point, and you'd take the larger value of . 



 

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .

This is more of a calculus question. We are asked to determine epsilon for which the given limit is true.





lim = √x^2+4 = 2, where delta (𝛿) = 1

x-> 0

~~~~~~~~~~~~~~~~~~~~~~







Hello,  in Calculus,  if we talk about the limits of functions,





the chain of events and the direction of thoughts is  DIFFERENT: 





        we first assign epsilon,  and then try to find delta.







Then the logic is straightforward,  clear, understandable and coincides with the logic of the definition of a limit.







Here you ask about opposite move:   you consider delta as given and ask about epsilon.







Again:  it is  OPPOSITE  to routine calculus consideration.







So,  I really do not understand the meaning of this exercise:   Is it designed to confuse a reader / (a student) ?







 

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