How to calculate critical value in hypothesis testing?
You wish to test the following claim ($H_a$) at a significance level of alpha=0.10. $H_o: \mu=70.4$ $H_a: \mu<70.4$ You believe the population is norma...
Published: Sep 06, 2026
Elementary product rule for Ito formula
In "Baxter, Rennie" book, there is an explanation of product rule for Ito formula. They apply Ito formula (without any details) to $$\frac{1}{2}((X_t + Y_...
Published: Sep 06, 2026
![Integrate $ \int \sqrt{\frac{x^3-3}{x^{11}}}\ dx$ [closed]](https://track.liberty.io/uploads/integrate-int-sqrt-frac-x-3-3-x-11-dx-closed_720.jpg)
Integrate $ \int \sqrt{\frac{x^3-3}{x^{11}}}\ dx$ [closed]
$$ \int \sqrt{\frac{x^3-3}{x^{11}}}\ dx $$ It seems like substitution could not do it. Is there another way?
Published: Sep 06, 2026
Condition of the mean value theorem
The usual formulation of the mean value theorem in a real analysis course is something like this: Let $f\colon [a,b] \to \mathbb{R}$ be continous on $[a,b...
Published: Sep 06, 2026
![How to find the limit of cos(2x)/x as x approaches zero [duplicate]](https://track.liberty.io/uploads/how-to-find-the-limit-of-cos-2x-x-as-x-approaches-zero-duplicate_720.jpg)
How to find the limit of cos(2x)/x as x approaches zero [duplicate]
Basicly the title. I know it's easy but I can't figure it out. [Edit] Not a duplicate has a 2x instead of x.
Published: Sep 06, 2026
Find, from first principle, the derivative of:
Find, from first principle, the derivative of: $$\log (ax+b)$$ My Attempt: $$f(x)=\log (ax+b)$$ $$f(x+\Delta x)=\log (ax+a\Delta x+b)$$ Now, $$f'(x)=...
Published: Sep 06, 2026
Why Two line coincide in the product of reflections
Example. Let $l$ and $m$ be two different lines intersecting at a point $P$. Show that $R_m R_l =R_{p, \theta}$ where $B$ is twice the directed angle $\al...
Published: Sep 06, 2026
How do you divide an inequality by another inequality?
The question I'm having trouble with is follows: Suppose you have already proved the proposition that, “If $a$ and $b$ are nonnegative real numbers, ...
Published: Sep 06, 2026
The rotation group $SO(3)$ may be mapped to a $2$-sphere by sending a rotation matrix to its first column. How can I describe the fibres of the map?
The rotation group $SO(3)$ may be mapped to a $2$-sphere by sending a rotation matrix to its first column. How can I describe the fibres of the map?
Published: Sep 06, 2026
How do you prove a number is prime?
I am a software engineer but try to keep up with maths as I really enjoyed the subject at school. I just saw a great TED talk: Why I fell in love with mon...
Published: Sep 06, 2026
