Question

Important: Please make sure assignment should be stapled if it is more than one sheet. The following deductions will be applied: you print the assignment sheet and write you solution on it. The submitted Submitting your assignment on a sheet other than given template: 2. Submitting your assignment loose and not stapling it. 1. %15 deduction %15 deduction 1. Use the Maclaurin (Taylor) series expansion for the sin x to estimate sin(/4) for the acceptable relative errors of 0.25 and 0.0025. sin x x + .. 3! 7! 9! 5! Please use the table formatting used in class to solve the problem

Answer 1

Ans)

sin(x) =x-(/3!)(a/5!) (x /7!)..

Exact value of  

sin (T/40.70710678118

Relative error = |(value obtained- true value )|/ (true value)

No of terms considered in the expansion Value of obtained Relative error

sin(r

1 0.785398163 11.0720 %

2   0.704652651 0.347066 %

3   0.707143046 0.0051286 %

4 0.70710647 0.000044 %

We can see that the first three values are in the acceptable range (0.25 - 0.0025).