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I have a very simple limit question.

$$\lim_{a\to\infty, b\to \infty} \frac{a}{a+b}$$

is the answer can't be determined?

I'd divided the numerator and denominator by $a$, and the denominator is $1 + {b \over a}$. So it depends on ${b \over a}$ and inf/inf is indeterminate?

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  • $\begingroup$ You are right . $\endgroup$ – Yves Daoust Oct 22 '15 at 16:17
  • $\begingroup$ In general $\lim_{a\to a_0}\lim_{b\to b_0}f(a,b)\neq \lim_{b\to b_0}\lim_{a\to a_0} f(a,b)$ hence you have to be careful in using the notation $\lim_{a\to +\infty,b\to +\infty}$. $\endgroup$ – Jack D'Aurizio Oct 22 '15 at 17:15
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The answer cannot be determined. Suppose b = r*a for some real number r. Then the limit is 1/r+1.

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