Friday, July 8, 2016

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 42

Determine the limit limx22|x|2+x, if it exists. If the limit does not exist, explain why.

The function contains an absolute value, therefore, we evaluate its left and right hand limit


For the right hand limitlimx2+2|x|2+x=limx2+2x2+xx=limx2+2x2+xx=




For the left hand limitlimx22|x|2+x=limx22(x)2+x)x=limx2\cancel2+x\cancel2+xx=limx21x=1


The left and right hand limits are different. Therefore, the limit does not exist

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