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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