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Nov
16
revised For the limit $\lim_{x\to -1}\frac{\sqrt{x+5}-1}{x+2}$, find $\delta$ that works for given $\epsilon$
edited title
Nov
16
comment How is $\lim_{n\to \infty}(1+\frac{2x}{n}+\frac{x^2+y^2}{n^2})^{\frac{n}{2}}=e^{\lim_{n\to \infty }(x+\frac{x^2+y^2}{2n})}$
@BozoVulicevic see update
Nov
16
revised How is $\lim_{n\to \infty}(1+\frac{2x}{n}+\frac{x^2+y^2}{n^2})^{\frac{n}{2}}=e^{\lim_{n\to \infty }(x+\frac{x^2+y^2}{2n})}$
added 732 characters in body
Nov
16
comment Random Variables, Die toss
@user273323 yes
Nov
16
answered Random Variables, Die toss
Nov
13
revised find the limit: $\lim_{n\to\infty}\int_{0}^{\infty} \frac{\sqrt x}{1+ x^{2n}} dx$
edited body
Nov
12
comment Calc 2 Limit Comparison Test
@zhw.OP needed a push for limit comparison test, not sure it is a mistake :-) but thanks for commenting
Nov
12
answered Is $\sqrt{x}$ uniformly continuous on $(0,1)$?
Nov
12
comment Is $\sqrt{x}$ uniformly continuous on $(0,1)$?
@abiessu OP likely means $f(x) \equiv \sqrt{2}$ and that would be defined for all real $x$, including $x \in (0,1)$...
Nov
12
revised Is $\sqrt{x}$ uniformly continuous on $(0,1)$?
deleted 4 characters in body; edited title
Nov
12
comment Calc 2 Limit Comparison Test
@zhw the word ratio in that expression refers not to the original ratio, but to the ratio of the approximated quantities, which is exactly $1/k^{5/2}$
Nov
12
revised confidence interval for median of an exponential distribution
added 60 characters in body
Nov
12
revised Regular functions $u(x,y)$ with $u_y=u_x^3$ are linear
added 11 characters in body
Nov
12
comment Inverse of Inner Product
@user3905813 you should be able to put another constraint on $x$. Notice our constraint $u \cdot x = 0$ means that $x = (x_1,x_2)$ satisfies $x_2 = 0$, so another constraint, linearly independent of the first one would do the trick.
Nov
12
comment Calc 2 Limit Comparison Test
@zhw. $$\frac{\sqrt{k}}{k^3+1} \approx \frac{k^{1/2}}{k^3} = \frac{1}{k^{5/2}}$$
Nov
12
revised Construct a function that is not Lebesgue-integrable but it is Riemann-interagrable
deleted 9 characters in body
Nov
12
comment Calc 2 Limit Comparison Test
@zhw. what do you mean? to day "their ratio looks like" just for the symmetry of expression?
Nov
12
answered How is $\sum_{k=0}^{\infty}\frac{e^{-1}}{(2k)!}=\frac{1+e^{-2}}{2}$
Nov
12
revised Calc 2 Limit Comparison Test
edited body
Nov
12
answered Calc 2 Limit Comparison Test