Taylor Martin
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 Oct26 comment Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable If you wanted to make it all workout to $\epsilon$ at the end, then just refine $P$ (if necessary) so that $|U(P,f)-L(P,f)|<(m_{f})^{2}\epsilon.$ But understand that this is not necessaty, since in general a quantity bounded by $C\epsilon$ for a constant that does not depend on $\epsilon$ is as good as being bounded by $\epsilon$ since both upper bounds can be made arbitrary small by sending $\epsilon\to0$. Oct26 comment Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable No - consider the case where $(m_{f})^{-2}<1$. Oct26 comment Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable Not sure what you mean. Oct26 answered Proving that if $f$ is Riemann integrable and $1/f$ is bounded then $1/f$ is Riemann integrable Oct21 answered Measure of the graph of a function such that the graph does not have measure zero. Oct21 answered derivative of $y=\sqrt{10^{5-x}}=u^{1/2}$ Oct14 comment 2. Differential equation with initial condition $\int(y-1)^{-1}\;dy\neq\ln(y-1)$ without further specifying $y$. Note that with $y=-3$ we get $\ln(-4)$ which is undefined. Oct14 answered 2. Differential equation with initial condition Oct10 comment When computing the CDF from a PDF, why is the integral bound a different variable? $F(x) =\int_{-\infty}^x f(t)\,dt$ The properties of a function remain the same whether you use $t,x,y,\alpha,u,etc.$ as the name for the dependent variable. It is strictly a matter of choice/convenience and to keep things clear for the exposition. $t$ in this case has nothing to do with time. Oct10 comment Evaluating $\sum\frac{1}{1+n^2+n^4}$ What do you mean evaluate? This sum has no easily attainable closed form, but it evidently converges by comparing to $a_{n}=n^{-2}.$ To get a sense of the challenges you face in evaluating this sum analytically, see math.stackexchange.com/questions/8337/… for the simpler case $\sum n^{-2}.$ Oct10 answered When computing the CDF from a PDF, why is the integral bound a different variable? $F(x) =\int_{-\infty}^x f(t)\,dt$ Oct9 answered Discount rates vs. Interest rate problem. Oct8 revised Given $\displaystyle f(x,y) = \frac{\sin (xy)}{x}$, $x \neq 0$, make $f(0,y)$ continuous. added 100 characters in body Oct8 answered Given $\displaystyle f(x,y) = \frac{\sin (xy)}{x}$, $x \neq 0$, make $f(0,y)$ continuous. Oct8 revised limit of solution of a autonomous differential equation at infinitive is a stationary point added 26 characters in body Oct8 answered limit of solution of a autonomous differential equation at infinitive is a stationary point Sep22 answered When to use $\mathbf{P}$ , and when to use $\mathbb{P}$ as the symbol for probability? Aug30 awarded Popular Question Jul2 awarded Curious Jul2 awarded Inquisitive