Homework Statement
In writing the definition of ##e## i.e. ##e=\displaystyle\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n##, why do we denote the variable by 'n' despite the fact that the formula holds for n∈(-∞,∞)? Is there any specific reason behind this notation i.e. does the variable have...
Although it gets better with experience, integrating an expression by hand is a really a trial and error procedure. A wrong substitution will get you nowhere in the available time. So I am wondering as to how they test your integration skills on GRE Mathematics Subject Test. Any help would be...
Homework Statement
I need to confirm if I correct in saying the following:
If f(x) is a function having the domain [a,b) as shown in the figure, then f(x) has several local maxima but none of them is global maximum, and f(x) does not have a global maximum.
Homework Equations and...
Homework Statement
Let A be a set of critical points of the function f(x).
Let B be a set of roots of the equation f''(x)=0.
Let C be a set of points where f''(x) does not exist.
It follows that B∪C=D is a set of potential inflection points of f(x).
Q 1: Can there exist any inflection points...
Some calculators say (-2)2/3 is equal to ##-\frac{1}{2^\frac{1}{3}}+i\frac{3^\frac{1}{2}}{2^\frac{1}{3}}## while others say its equal to ##4^{\frac{1}{3}}## i.e. ##|-\frac{1}{2^\frac{1}{3}}+i\frac{3^\frac{1}{2}}{2^\frac{1}{3}}|##.
I think I am right to imply from above that (-2)2/3 does have an...
- This may be a stupid question as I am totally new to the concept of interest. I don't even know if my question is valid.
- Figure is given below for referenceSuppose I deposit some money in a bank that pays compound interest on yearly basis. If I decide to withdraw my amount at the end of 3.5...
Stephen Wolfram (creator of Wolfram Mathematica) earned a PhD in theoretical physics before he completed his undergraduate. He had taught himself physics and was publishing papers at a very young age (13 as far as I remember [look it up!]). In college, he combined some of his papers into his PhD...
You can't really understand elementary particle behavior when your brain limited to classical mechanics. Please upgrade your brain to a quantum version :smile: You can start here: https://www.bulletproofexec.com/bulletproof-upgraded-brain-octane/
Considering the particle-wave duality theory...