André Nicolas
Reputation
396,200
393/400 score
 1d comment If $f'(x)\rightarrow \infty$ then $f(x)\rightarrow\infty$? You are welcome. It can be somewhat tricky to go from "local" information (the derivative) to "global" information. The MVT does the job, as would integration. 1d comment Find area of shaded area in curve with range of values for $y$ Hint: The right half of the shaded region is a rectangle plus the region below $y=32-2x^2$, above $y=14$, from $x=2$ to $x=4$. 1d revised If $f'(x)\rightarrow \infty$ then $f(x)\rightarrow\infty$? added 11 characters in body 1d answered If $f'(x)\rightarrow \infty$ then $f(x)\rightarrow\infty$? 1d comment If $f'(x)\rightarrow \infty$ then $f(x)\rightarrow\infty$? Not true. Example, $f(x)=x$. There are much "wilder" examples. Just knowing that $f(x)\to\infty$ as $x\to\infty$ tells us little about $f'(x)$. 1d comment Prime number theory. A start: Suppose to the contrary that some $d\gt 1$ divides both.Then some prime $p$ divides both. We have $p$ divides $ab$ so $p$ divides $a$ or $p$ divides $b$. (i) Show that $p$ divides $a$ and $p$ divides $ax+by$ leads to a contradiction; (ii) Do the same for $p$ divides $b$ and $ax+by$. 1d revised Find the sum using added 967 characters in body 1d revised normal approximation with continuity correction added 547 characters in body 1d comment normal approximation with continuity correction You are welcome. I will add a "practical" remark about the continuity correction. 1d comment Number of ways to get from a point to another one in the plane Our path can be represented by an $m+n$-letter "word" made up of $m$ occurrences of the letter R (right) and $n$ occurrences of the letter U. How many such words are there? 1d answered normal approximation with continuity correction 1d revised Find the sum using added 12 characters in body 1d comment Find the sum using @patrickh: You are not mistaken! 1d answered Find the sum using 1d answered How many draws to have a 90% chance of getting the ace of spades? 2d comment Factor $x^6+x^5+x^4+x^3+x^2+x+1$ in $\mathbb{F}_2[x]$ $(x^3+x^2+1)(x^3+x+1)$. These two factors are irreducible, since they are cubics with no root. 2d comment What number(s) is unequal to itself In the standard axiomatizations of the predicate calculus with equality, one common axiom is $\forall x(x=x)$. 2d comment Can a field be isomorphic to its subfield but not to a subfield in between? It has been a while, and I am post dinner and wine. They are not isomorphic as fields, since $F$ is algebraically closed but $E$ is not. 2d comment Prove surface area of a sphere using solid of revolution surface area formula. For the first one you are rotating the top half of $x^2+y^2=1$, that is, $y=\sqrt{1-x^2}$. 2d comment Factoring polynomials in $\Bbb Z_n$ @Nid: The quadratic mod $10$ has an additional factorization that I mentioned above.