Tuesday, October 24, 2017

calculus - Evalutating limxto+inftysqrtx2+4x+1x





I'm looking to evaluate



limx+x2+4x+1x



The answer in the book is 2. How do I simply evaluate this problem?




I usually solve limits such as this with the short cut method, i.e (Numerator degree < Denominator degree) = 0 ; (Numerator degree = Denominator degree )= take ratio of leading coefficients; (Degree numerator > degree denominator )= take leading terms and use algebra to simplify and then plug in or +
Please keep in mind that I do not know L'Hopital's rule.


Answer



limxx2+4x+1x=limx(x2+4x+1x)x2+4x+1+xx2+4x+1+x=limx(x2+4x+1)x2x2+4x+1+x=limx4+1x1+4x+1x2+1=41+1


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