Wednesday, 28 October 2015

limits - Find limxtoinftyfrac(x1)2x+1




Find lim




If I divide whole expression by maximum power i.e. x^2 I get,\lim_{x\to -\infty} \frac{(1-\frac1x)^2}{\frac1x+\frac{1}{x^2}}

Numerator tends to 1 ,Denominator tends to 0



So I get the answer as +\infty



But when I plot the graph it tends to -\infty



What am I missing here? "Can someone give me the precise steps that I should write in such a case." Thank you very much!



NOTE: I cannot use L'hopital for finding this limit.


Answer




Hint: Write \frac{x^2\left(1-\frac{1}{x}\right)^2}{x\left(1+\frac{1}{x}\right)}


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