# Limit question: $\lim_{x\to \infty}f(x),\;\; \lim_{x\to -\infty}f(x)$?

Assuming $$f(x)=ax^3+bx^2+cx+d$$

show that $\lim_{x\rightarrow\infty}f(x)$ and $\lim_{x\rightarrow -\infty}f(x)$ exists, find the limits.$a,b,c,d\in\mathbb{R}$

Well, I think the limits exists in extended real line and their values are simply $+\infty$ and $-\infty$. If I am missing something please help.

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You are right. The point is that $\lim\limits_{x\to\infty}f(x)/x^3 = \lim\limits_{x\to-\infty}f(x)/x^3 = a$ and you know how $x^3$ behaves. Here, of course, it is important that $a \neq 0$ - otherwise you have $x^2$ term which is leading if $b\neq 0$ etc. – S.D. Nov 30 '12 at 14:22
Unless all the coefficients besides d are 0, the limits should be $\pm\infty$. If a is 0 and b is not, you get the same limits for both ends. If a is not 0 or if a and b are both 0 , you get limits with opposite sign, with the concrete results depending on the sign of a or c respectively. If every coefficent but d is zero, the limits on both end simply are d – kram1032 Nov 30 '12 at 14:26
okay thank you... – La Belle Noiseuse Nov 30 '12 at 14:27