Limit as x approaches 0 of (square root(4+x^4)-2)/x^4)

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The limit as x approaches 0 of (sqrt(4+x^4)-2)/x^4 can be solved by rationalizing the numerator. This involves multiplying both the numerator and denominator by (sqrt(4+x^4)+2). Applying the difference of squares formula, (a+b)(a-b)=a^2-b^2, simplifies the expression effectively. The final result of this limit calculation is 0.

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limit as x approaches 0 of (square root(4+x^4)-2)/x^4)
it says to solve algebraically by rationalizing the numerator
 
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To rationalize it multiply numerator and denominator by sqrt(4+x^4)+2. Use (a+b)*(a-b)=a^2-b^2.
 

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