User talk:Sashafklein

Strangely, I dont see a welcome message here.. So here goes:

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Hi Sashafklein!
Sorry for the late response, I've been a little busy. Nikon is not really my forte (I'm a canon man!), but as a general guide I would advise to buy as good a lens as you can afford. Personally I would prefer buying one really good lens rather than three mediocre ones. That's just a personal taste, but if you want to become a more serious photographer I would advise you to do the same. Often your lens is the bottleneck of your camera. Poor lens and you can be shooting with the 1Ds MkII and get crummy photos. Also stay away from wide to extreme tele like 28-300mm. Unless they are expensive chances are they will be pretty crummy. I also strongly recommend a visit to Fredmiranda - you can get good reviews and advice there. Bokeh wise, if you are using a DSLR, you'll get good results from most lenses. For really good bokeh, get a lens which has a max aperture of f/2.8 or higher. Again you will get what you pay for.
Thanks a lot for the comments on my photos, stuff like that is what makes me keep going! Good luck and I hope to see you around with your new camera/len(s)! --Fir0002 12:52, 3 August 2006 (UTC)[reply]

Good day, Sashafklein. I'm in my school's library right now, and the bell's going to ring is 5 seconds, which means that I can't delineate, but there is a way to get a Riemann sum on a TI-83. I'll get back to you if you haven't figured it out yet. —The preceding unsigned comment was added by Gracenotes (talk • contribs) 18:19, 5 December 2006 (UTC).[reply]

NOTE: if you just want what to enter into your calculator, and not the derivation, skip to the last paragraph.

Hm, there goes the autosign bot again. (Gracenotes cowers in chagrin.) Well, I'm sorry that your teacher makes you use upper and lower Riemann sums instead of left and right, as you noted here. Just so you know, I believe that the AP Exam requires that you use left and right.

So, according to your post, you want to easily calculate the upper or lower Riemann sum on an interval for a given function. Your function name is ${\displaystyle f(x)}$, the interval is on ${\displaystyle [A,B]}$, and you have a subinterval of ${\displaystyle \Delta x}$. You have an enterable function for ${\displaystyle f(x)}$ and real numbers for A, B, and ${\displaystyle \Delta x}$?

Here are a couple of basic functions you'll need: the ${\displaystyle seq()}$ function, which can be found by pressing [2nd] [STAT] (at LIST), under the OPS submenu at number 5. ${\displaystyle seq(f(x),x,A,B,\Delta x)}$ yields a list of numbers on screen. The first number is ${\displaystyle f(x)}$, the second is ${\displaystyle f(x+\Delta x)}$, the third is ${\displaystyle f(x+2\Delta x)}$, and so on, so long as ${\displaystyle f(x+n\Delta x)\leq f(B)}$. (${\displaystyle n}$ is a whole number here. It just so happens to be ${\displaystyle \Delta x/(B-A)}$.) From now on I'll assume that there are n equal subintervals, each with width ${\displaystyle \Delta x}$

The ${\displaystyle sum()}$ function helps you tremendously. It takes any list, and sums up the contents. (Do you see where I'm going with this :) ?) For example, if you create list L1 (by going to [STAT] [Edit...]), you can sum up the contents by asking the calculator ${\displaystyle sum(L1)}$. The ${\displaystyle sum()}$ function is located at [2nd] [STAT] (at LIST), under the MATH submenu at number 5.

To calculate a left hand Reimann sum, type in

${\displaystyle \operatorname {sum} (\operatorname {seq} (\Delta x\cdot f(x),x,A,B,\Delta x))}$

This will create a list ${\displaystyle \{\Delta x\cdot f(A),\Delta x\cdot f(A+\Delta x)...\Delta x\cdot f(B-\Delta x),\Delta x\cdot f(B)\}}$, which is the Reinmann sum for f(x) on that interval. Then it sums it up. I'm sure that you can figure out how to do right hand and mid, from that. The trapezoid rule requires a bit more complication, but I have faith in you. :)

I need to show you two last functions before I answer your question. You know how the calculate the minimum or maximum value of a function, right? Enter a function into Y1, go to F4 ([2nd] [Trace]), click on 3 or 4, wait for the function to graph, enter your endpoints, and you get the max or min value. You can do this without graphing the function, with the functions fMin() and fMax(). Both are in the MATH menu. To get the X value which yields the maximum function value on a function ${\displaystyle f(x)}$ on the interval from A to B, type ${\displaystyle \operatorname {fMax} (f(x),x,A,B)}$. For the minimum value, use fMin instead. To actually get the the minimum function value, for example, type ${\displaystyle f(\operatorname {fMax} (f(x),x,A,B))}$

The upper Reinmann sum: So to sum together the maximum values of ${\displaystyle f(x)}$ on the interval <math[A,B]</math>, with ${\displaystyle n}$ equal subintervals of width ${\displaystyle \Delta x}$, type

${\displaystyle \operatorname {sum} (\operatorname {seq} (\Delta x\cdot f(\operatorname {fMax} (f(x),x,x,x+\Delta x)),x,A,B,\Delta x))}$

For the lower sum, use

${\displaystyle \operatorname {sum} (\operatorname {seq} (\Delta x\cdot f(\operatorname {fMin} (f(x),x,x,x+\Delta x)),x,A,B,\Delta x))}$

That's all. No program required. The smaller ${\displaystyle \Delta x}$ gets, the more accurate, and the more time it'll take for your calc to do it. To begin with, even a simple calculation takes a LONG time. But better than doing it by hand, I suppose.

Example: calculate upper limit on sine function from 0 to pi with subinterval of pi/4? Try

${\displaystyle \operatorname {sum} (\operatorname {seq} (\pi /4\cdot \sin(\operatorname {fMax} (\sin(x),x,x,x+\pi /4)),x,0,\pi ,\pi /4)}$

I got 2.681512524. For the minimum I got 1.110731688. If yours is different, I may have done something wrong, or you didn't enter it right. Good luck, and happy calculating! (Thank goodness for the Fundamental Theorem of Calculus, though.)

And upper/lower sums are equivalent to left/right when the function has either a completely positive or completely negative derivative on the interval.

If you got this message, please respond to let me know you did. Thanks, and please contribute to Wikipedia!

Gracenotes ^T § 21:55, 5 December 2006 (UTC)[reply]

Actually, the commands that I gave you only apply if the beginning of the subinterval is less than B. This may not be a desired result, you'd also want the end of the subinterval to be less than B. So the following will work for mathematical purposes:

${\displaystyle \operatorname {sum} (\operatorname {seq} (\Delta x\cdot f(\operatorname {fMax} (f(x),x,x,x+\Delta x)),x,A,B-\Delta x,\Delta x))}$

Or

${\displaystyle \operatorname {sum} (\operatorname {seq} (\Delta x\cdot f(\operatorname {fMin} (f(x),x,x,x+\Delta x)),x,A,B-\Delta x,\Delta x))}$

If you really don't care, I don't mind. :) At least I learned something. --Gracenotes ^T § 17:40, 6 December 2006 (UTC)[reply]

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Merry Christmas and Happy Holidays Sashafklein! | AndonicO ^{Talk | Sign Here} 01:04, 15 December 2006 (UTC)[reply]

May you and your family have a Merry Christmas, as well as any other Holiday you may celebrate. I hope that warmth, good cheer, and love surround you during these special days. May God bless you during the Holidays. | AndonicO Talk | Sign Here 01:04, 15 December 2006 (UTC)[reply]

File:Julekort.jpg

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