Sin(x) can be expressed by Taylor series as below x5 x3 + 3! sin(x) =D Σn=o° (-1)"x2n+1 x7 (2n+1)! 5! 7! Write a F90 program to calculate sin(x) taking appropriate number of terms. Hints: • X always in radian • Let y=sin(x) • You have to have two do loops

Q: Confirm that summation d/36 ϕ(d) = 36 and summation d/36 (-1)^(36/d) ϕ(d) = 0

A: We have to confirm that ∑d/36φ(d)=36 and ∑d/36(-1)36/dφ(d)=0.

Q: 4) (x²D² + xD-1)y=16x³ y(1)=-1 y'(1)=1

A:

Q: 7.29. (a) Expand f(x) = cos z, 0 << r, in a Fourier sine series.

A:

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on…

A: (a) Given that F(t)=2tF(−t)=−2t=−F(t)Therefore F(t) is an odd function.F(t) extends to [−π,π] so the…

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

A: