Monday, 14 July 2014

calculus - Find the value of : limxtoinftyfracsqrtx1sqrtx2sqrtx2sqrtx3




I'm trying to solve evaluate this limit



limxx1x2x2x3.



I've tried to rationalize the denominator but this is what I've got



limx(x1x2)(x2+x3)



and I don't know how to remove these indeterminate forms ().




EDIT: without l'Hospital's rule (if possible).


Answer



Fill in details:



As x we can assume x>0 , so:



x1x2x2x3=x2+x3x1+x2=12x+13x11x+12xx1



Further hint: the first step was multiplying by conjugate of both the numerator and the denominator.



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