Excluded Posted November 30, 2011 Report Share Posted November 30, 2011 (edited) observe the pattern in the results, describe it in words. then, formulate a general statement. at this stage, x=1 so a^x=a, so at this stage you do not know yet that the formula is a^x. you only know that it's a. and then, you'll test for other values of x, and you find that hey it doesn't just approach a, it approaches a^2 when x=2, it approaches a^3 when x=3, etc. so then you conclude that it's a^x for x=2 and a=2, the sum is 2? you sure? maybe you made a calculation mistake? oh ok thank you very much, so for the stage i am at i just have to right that S(inifinity)= a i also want to ask you, for the second part, it says that we have to graph between T9(2,x) and x what does that mean i plot what against what? i plot the value of Sn for different values of x? so i find T9(2,2) and the S(infinity) of this is one point? thank you very much! No what you would do is calculate each sum to the 9th term of different positive x terms in one graph. For example let x = 1, 2, 3, 4, 5 and calculate the S9 for each one of them. That should be all in one graph. so x axis = x value and y axis = T9 (2, x) value (aka S9 ) So rather than graphing/calculating S1, S2, S3.... S10, you're going straight at S9. Edited November 30, 2011 by Excluded 1 Reply Link to post Share on other sites More sharing options...
hjälpmig Posted November 30, 2011 Report Share Posted November 30, 2011 I've tested several x values, including x= -2. Now, T approaches a^x buuuut the sum T changes between negative and positive. Does this mean x>0 and why? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 30, 2011 Report Share Posted November 30, 2011 I've tested several x values, including x= -2. Now, T approaches a^x buuuut the sum T changes between negative and positive. Does this mean x>0 and why?yes it does, because when x<=0 your general statement doesn't work. Reply Link to post Share on other sites More sharing options...
hjälpmig Posted November 30, 2011 Report Share Posted November 30, 2011 (edited) But why doesn't it work?Cause when graphing it I can see that it's all messed up, but can I merely exclude x < 0 on the basis that T changes between negative and positive?Also, really what I need help with is saying in a smart way that x> 0 haha Edited January 2, 2012 by Jirashimosu Merging three posts Reply Link to post Share on other sites More sharing options...
vaemma Posted December 2, 2011 Report Share Posted December 2, 2011 i am completely lost when i look at the questions it looks like it is written in an alien language . all i need to know is where/ how to start it.please and thank you. Reply Link to post Share on other sites More sharing options...
dessskris Posted December 2, 2011 Report Share Posted December 2, 2011 i am completely lost when i look at the questions it looks like it is written in an alien language . all i need to know is where/ how to start it. please and thank you. read this post --> in fact you should read pages 7-10, most of the tips were posted there. good luck! Reply Link to post Share on other sites More sharing options...
chicheto93 Posted December 3, 2011 Report Share Posted December 3, 2011 (edited) After 1 pack of cigarettes and 8 hours I understood this thanks to Desy Glau!!!!! Thank you so much!!! However another question that I have is. On the second page when they ask us to plot the relation between T9 and x - I am thinking of plotting the 5-6 different values of X that I have chosen on the X - axis and plotting the sum of the(5-6 different) nine terms on y - axis. Is that correct? Because for example when x = 9 Sum of the first nine terms = 460.1 and the expected value is 2^9=512 which is actually met on the 17th term and not the 9th. So what should I plot? Or is it like different positive values of X on the x-axis and only the different 9th terms on the y-axis? NOT the sum of the first 9 terms but only the 9th term? What is correct? Please help Oh yeah and what type of graph should it be? Should I include trendline or no? Edited December 3, 2011 by chicheto93 Reply Link to post Share on other sites More sharing options...
dessskris Posted December 4, 2011 Report Share Posted December 4, 2011 After 1 pack of cigarettes and 8 hours I understood this thanks to Desy Glau!!!!! Thank you so much!!! However another question that I have is. On the second page when they ask us to plot the relation between T9 and x - I am thinking of plotting the 5-6 different values of X that I have chosen on the X - axis and plotting the sum of the(5-6 different) nine terms on y - axis. Is that correct? you're welcome, and yep that's right Because for example when x = 9 Sum of the first nine terms = 460.1 and the expected value is 2^9=512 which is actually met on the 17th term and not the 9th. So what should I plot? you should plot the T9 (the sum of the first 9 terms) Or is it like different positive values of X on the x-axis and only the different 9th terms on the y-axis? NOT the sum of the first 9 terms but only the 9th term? What is correct? Please help the sum of the first 9 terms! not just the 9th one. Oh yeah and what type of graph should it be? Should I include trendline or no? scatter graph, hmmm yess try to put a nice trendline Reply Link to post Share on other sites More sharing options...
IBmath_student Posted December 4, 2011 Report Share Posted December 4, 2011 It says to calculate the sum Sn of the first n terms of the above sequence for 0-10for this should you get 10 different answers?Do you find what the first term is, then the first term+the second, then first+second+third, and so on?Is n what the numerator is raised to?I just don't understand how to start Reply Link to post Share on other sites More sharing options...
dessskris Posted December 5, 2011 Report Share Posted December 5, 2011 It says to calculate the sum Sn of the first n terms of the above sequence for 0-10for this should you get 10 different answers?yeah, S1, S2, S3, ... , S9 and S10Do you find what the first term is, then the first term+the second, then first+second+third, and so on?correct.Is n what the numerator is raised to?I just don't understand how to startn is the thing in the denominator (n!) and also the power in the numerator. 1 Reply Link to post Share on other sites More sharing options...
hraouf1 Posted December 14, 2011 Report Share Posted December 14, 2011 How do i test the validity of the general statement , and discuss limitations and explain all this (second page) and the general statement for the first part is a^x but how do i get the 2nd part's general statement? Reply Link to post Share on other sites More sharing options...
britney spears is awesome Posted January 2, 2012 Report Share Posted January 2, 2012 (edited) Hey when it says that the T9(a, x) notation means the sum of the first nine termsdoes "first nine terms" refer tot0, t1, t2, t3, t4, t5, t6, t7, t8, and t9or just t1, t2, t3, t4, t5, t6, t7, t8, t9because without t0 = 1 added to the sum....the general statement doesn't really workORcould it mean "first nine terms" as int0, t1, t2, t3, t4, t5, t6, t7, t8 only? Edited January 2, 2012 by Jirashimosu merging consecutive posts Reply Link to post Share on other sites More sharing options...
SSJ5Goku Posted January 2, 2012 Report Share Posted January 2, 2012 Hey when it says that the T9(a, x) notation means the sum of the first nine terms does "first nine terms" refer to t0, t1, t2, t3, t4, t5, t6, t7, t8, and t9 or just t1, t2, t3, t4, t5, t6, t7, t8, t9 because without t0 = 1 added to the sum....the general statement doesn't really work OR could it mean "first nine terms" as in t0, t1, t2, t3, t4, t5, t6, t7, t8 only? The way I see it, it's the "first nine terms" as in 0 < n < 9. I mean, the sum of the first 10 terms would probably be from 0 to 10, right? Though don't quote me on it Now for my own question (I'm not sure if it's been addressed yet, so I apologize if it has): why do they specifically ask us to consider x=1,a=2 and x=1,a=3 and THEN ask us to consider various other sequences where x=1? Is there any purpose to it or is it just so that we get the hang of things? Maybe I've been spending too much time in ToK... Reply Link to post Share on other sites More sharing options...
Victoria Miller Posted January 3, 2012 Report Share Posted January 3, 2012 i have this feeling that my graphs are wrong but I am unsure how to fix them. because as n aproaches infinity, i got that Sn approaches a. right? but my graph is going the wrong way :/ Reply Link to post Share on other sites More sharing options...
mjcat Posted January 3, 2012 Report Share Posted January 3, 2012 How do i test the validity of the general statement , and discuss limitations and explain all this (second page) and the general statement for the first part is a^x but how do i get the 2nd part's general statement?I've got the same question! Can anyone help?And also can anyone give me hints as to how to provide an informal justification for the general statement? Reply Link to post Share on other sites More sharing options...
El Che Posted January 3, 2012 Report Share Posted January 3, 2012 To test the validity of your general statement you should give different values for a and x, and then represent them in the way you have previously done. Don't forget to calculate the values for the first nine terms only. For scope and/or limitations consider real numbers, irrational numbers, negative integers, and etc to see whether they would work for your general statement. 1 Reply Link to post Share on other sites More sharing options...
Victoria Miller Posted January 3, 2012 Report Share Posted January 3, 2012 WOO HOO I just finished. and desy glau you rock as you taught me how to use excel hahaha Reply Link to post Share on other sites More sharing options...
robawalsh Posted January 31, 2012 Report Share Posted January 31, 2012 How do you enter factorials (!) into the TI-84? Reply Link to post Share on other sites More sharing options...
sk2801 Posted February 26, 2012 Report Share Posted February 26, 2012 HEY DESY GLAU!!! i have a quick question. could u explain the deal with the taylor sequence again. how does that incorporate into all of this? Thanks a lot Reply Link to post Share on other sites More sharing options...
janusshan.p Posted February 27, 2012 Report Share Posted February 27, 2012 On the second page where it says the first nine terms does that mean :The sum of t0 --> t8orThe sum of t0-->t9Thanks Reply Link to post Share on other sites More sharing options...
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