Program for Sin(x^2) MacLaurin Series

[Einstein2.0]

I'm currently attempting to design a program on my ti-84 calculator (ti-nspire w/ 84 faceplate) to provide an approximation of the sin(x^2) as accurate as I would like the sum the reach. I attempted to input a formula for such, sum(seq((-1)^(Z-1)*X^(4Z-2)/(2Z-1)!, Z, 1, n, 1)), "Z" being the variable of the series whose end would be determined by my input of "n", and I wanted the program to display the series INCLUDING the variable "X," hence, displaying the MacLaurin approximation of sin(x^2). I hoped to possibly graph this and use the method in some way to provide an approximate integration of sin(x^2). Could anyone let me know if this is possible or even point me in a better direction? Sorry this question has to be so long.

 

[mathman]

Start with the series for sin(y) and then let y = x². I may be missing something in your description.

 

[Einstein2.0]

Start with the series for sin(y) and then let y = x². I may be missing something in your description.

It's the fact that the calculator won't display the series w/ the variable "X" that's my real problem. I'm not really sure if the calculator can do something like that.

 

[mathman]

It's the fact that the calculator won't display the series w/ the variable "X" that's my real problem. I'm not really sure if the calculator can do something like that.

I can't help you, since I have never used a TI-84 calculator.

 

[alphy]

I think it's great that you are trying to develop a program to approximate the MacLaurin series for sin(x^2). This can be a useful tool for approximating the value of sin(x^2) and potentially for integration purposes.

Your approach of using the sum(seq()) function on your calculator is a good start. However, there are a few things to consider. First, the formula for the MacLaurin series of sin(x^2) is actually a bit different from what you have inputted. It should be sum(seq((-1)^(n)*x^(4n+2)/(2n+1)!, n, 0, k, 1)), where "k" is the number of terms you want to include in the series. This formula will give you the terms of the series up to the kth term.

Secondly, you mentioned wanting to display the series including the variable "x". This may be a bit more complicated on a calculator, but you can try using a loop to input different values of "x" and then display the series for each value. Alternatively, you could also try using a graphing calculator to graph the series and visually see how it approximates sin(x^2).

Lastly, I would suggest exploring other methods for approximating integrals, such as the trapezoidal rule or Simpson's rule, which may be more accurate and easier to implement on a calculator. Overall, it's great that you are exploring the applications of the MacLaurin series and I encourage you to continue learning and experimenting with different methods.