SOLUTION: 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

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Question 1192696: 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
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!



The definition of a limit is  lim(x-->a) +f%28x%29+ = L    if:



        |f(x)-L| < epsilon   for  0 < |x-a| < +delta+





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

    f(-1) = sqrt%28%28-1%29%5E2+%2B+4%29+=+sqrt%285%29+

    f(1) = sqrt%28%281%29%5E2+%2B+4%29+=+sqrt%285%29+



So the exact value of epsilon+ is +f%28x%29-L+ = +highlight%28+sqrt%285%29+-+2+%29+  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 epsilon.

Answer by ikleyn(52777) About Me  (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) ?