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Nov
13
comment Increasing and Decreasing Functions
You can do it, but can you explain it???
Nov
13
comment Transcendence of $\sqrt{\pi}$
See this? en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theorem
Nov
13
answered Use partial fractions to find the integral.
Nov
13
comment Describing relations
@anon: so the Socratic method works!
Nov
13
comment Describing relations
WHAT IS "A"?
Nov
13
answered Help in a calculus question
Nov
13
comment Help in a calculus question
Oh. You can think of it in terms of the average value of a function which is defined as an integral a few lines down on that page. But if the "value" is the rate of change, you are integrating the derivative, and the fundamental theorem of calculus gives us $\dfrac{f(b)-f(a)}{b-a}$
Nov
13
comment Help in a calculus question
Could you be more specific? The slope of the line through the points $(a,f(a))$ and $(b,f(b))$ is the average rate of change on the interval $[a,b]$.
Nov
13
comment Use partial fractions to find the integral.
I fully understand what you did. The way that this is presented is more like guessing than following a method. OP asked for the method of partial fractions, not magically coming up with a clever version of zero to add... Anywho. OP, try $x=1$.
Nov
13
comment Help in a calculus question
Of course, this simplifies...
Nov
13
comment Help in a calculus question
You do not sum and divide by two. The average rate of change is $$\dfrac{1}{b-a}\int_a^b f'(t)dt$$
Nov
13
comment Given positive integers $m$ and $n$, if $m | n$ then $2^m -1 | 2^n -1$
Granted, google gave me this: math.stackexchange.com/questions/529111/…
Nov
13
comment Given positive integers $m$ and $n$, if $m | n$ then $2^m -1 | 2^n -1$
@Jim: if I had any clue how to search math-y stuff on here, I could have provided many more (and more helpful)links!
Nov
13
comment Given positive integers $m$ and $n$, if $m | n$ then $2^m -1 | 2^n -1$
This has surely been asked and answered here many times. The closest I could find, though, is math.stackexchange.com/questions/561077/…
Nov
13
comment Use partial fractions to find the integral.
To expect the typical student to come up with such "notes" is ludicrous. Maybe you can do polynomial division/partial fractions in your head, but most students cannot...
Nov
13
comment Solving for $y$ in $y= 14x + 1000 = y= 16x + 800$
FYI - from the second line, you need to "solve a linear equation". That is something that many here can teach, but you might be better served by a web search/YouTube/khan academy...
Nov
11
comment If $\lim f(x)$ exists and $\lim g(x)$ do not, when $x$ approaches $a$ , why $\lim[f(x)+g(x)]$ does not exist?
"... the proper thing to say is that the function 'diverges' or 'grows without bound'..." wiki
Nov
11
comment If $\lim f(x)$ exists and $\lim g(x)$ do not, when $x$ approaches $a$ , why $\lim[f(x)+g(x)]$ does not exist?
No, but there are other ways for a limit to not exist. Actually, you've added two functions without limits. Did the OP ask about that?
Nov
11
comment If $\lim f(x)$ exists and $\lim g(x)$ do not, when $x$ approaches $a$ , why $\lim[f(x)+g(x)]$ does not exist?
$\infty \in \mathbb{R}$?
Nov
11
comment Riddle that doesn't make sense and makes sense at the same time
Is the solution unique?