Saturday, 28 December 2013

calculus - Solving limit without L'Hôpital



I need to solve this limit without L'Hôpital's rule. These questions always seem to have some algebraic trick which I just can't see this time.



limx05x+25x



Could someone give me a hint as to what I need to do to the fraction to make this work? Thanks!


Answer



limx05x+25x=limx0(5x+25)(5+x+25)x(5+x+25)=limx025(x+25)x(5+x+25)=110


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