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anonymous
 one year ago
Does anyone know why the function f(x)= 1/(x1)^4 the limit as it approaches to 1 is infinite. I thought that in this case we should use the oneside limits because when x=1 the denominator will be 0.
anonymous
 one year ago
Does anyone know why the function f(x)= 1/(x1)^4 the limit as it approaches to 1 is infinite. I thought that in this case we should use the oneside limits because when x=1 the denominator will be 0.

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phi
 one year ago
Best ResponseYou've already chosen the best response.1if you get the same value for both the left and rightsided limit, then that value is the limit. In this case approaching from the left side of 1 (below 1) \[\lim_{x \rightarrow 1^} \frac{ 1 }{ (x1)^4 }=\frac{ 1 }{ 0 }= \infty\] notice that though 0.9991.000 = 0.001 is negative, after raising to an even power (4 in this case) we get a positive number that approaches 0 similarly, the other side also gives \[\lim_{x \rightarrow 1^+} \frac{ 1 }{ (x1)^4 }=\frac{ 1 }{ 0 }= \infty\] example: 1.001 1.000= 0.001, and raised to the 4th power, is a small positive number that approaches 0, and consequently the fraction approaches infinity.
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