In an exam we have

Question (5points) find $\lim_{x\to\infty}(x-\sqrt{x})$.

A student answered: $\lim_{x\to\infty}(x-\sqrt{x}) =\lim \sqrt{x}(\sqrt{x}-1)=\infty \cdot\infty=\infty$.

My question is: how many point you will give the student? A professor in our department says it should be zero or one out of five, arguing that the student does not understand what are limits for and treat them as real numbers.

I think 4/5 is fair. Because he almost did everything except that he did not mention that the product of two infinite limits is infinite.




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