(Section 2.5: The Indeterminate Forms 0/0 and ±/±) 2.5.5 Solution to b)limx±0fx()=limx±0x2²1x2²xLimit Form ²10³´µ¶·¸=limx±0x+1=limx±0x+1xObserve: limx±0+x+1xLimit Form 10+²³´µ¶·=¸, and limx±0²x+1xLimit Form 10²³´µ¶·¸=²¹. Therefore, limx±0does not exist (DNE), not even as ±or ±². Commentary on b)• Here, the cancellation / dividing out of the x±1factors merely makes it more convenient when we analyze the limit as x±0. • Why does the limit not exist here as a real number?
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lim, Limit of a function, Indeterminate form