document.write( "Question 1192696: This is more of a calculus question. We are asked to determine epsilon for which the given limit is true.\r
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\n" ); document.write( "\n" ); document.write( "lim = √x^2+4 = 2, where delta (𝛿) = 1
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Algebra.Com's Answer #824593 by math_helper(2461) $\"\"$ $\"About$

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document.write( "The definition of a limit is  lim(x-->a)  = L    if:\r
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document.write( "        |f(x)-L| <    for  0 < |x-a| < \r
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document.write( "So here,  = 1, centered at x=0, so we need to evaluate f(-1) and f(1): 
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document.write( "    f(-1) = 
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document.write( "    f(1) = \r
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document.write( "So the exact value of  is  =   or approx. 0.2361\r
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document.write( "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 . \r
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