Write a program in C to find the root of the equation 𝒇(𝒙) = 𝒙𝟑 − 𝒙 − 𝟐 using the Bisection Method. Output

Write a program in C to find the root of 𝒇(𝒙) = 𝒙𝟑 − 𝒙 − 𝟐 using the Regula Falsi Method. Output

Write a program in C to find the root of 𝒇(𝒙) = 𝒙𝟑 − 𝒙 − 𝟐 using the Newton–Raphson Method Output

Write a program in C to find one root of the polynomial x³ − 𝟔x² + 𝟏𝟏x − 𝟔 = 𝟎 using the Birge–Vieta Method. Output

Write a program in C to solve the system of equations using the Gauss Elimination Method: 𝟐𝒙 + 𝒚 − 𝒛 = 𝟖 − 𝟑𝒙 − 𝒚 + 𝟐𝒛 = −𝟏𝟏 − 𝟐𝒙 + 𝒚 + 𝟐𝒛 = −3 Output

Write a program in C to solve the system of equations using the Gauss–Jordan Method:𝟐𝒙 + 𝒚 − 𝒛 = 𝟖 − 𝟑𝒙 − 𝒚 + 𝟐𝒛 = −𝟏𝟏 − 𝟐𝒙 + 𝒚 + 𝟐𝒛 = −3 Output

Write a program in C to solve the following system using the Gauss–Seidel Method:𝟏𝟎𝒙 + 𝒚 + 𝒛 = 𝟏𝟐𝒙 + 𝟏𝟎𝒚 + 𝒛 = 𝟏𝟑𝒙 + 𝒚 + 𝟏𝟎𝒛 = 𝟏4 Output

Write a program in C to find the value of 𝒚 for 𝒙 = 𝟑 given the data using Lagrange’s Interpolation:x: 1, 2, 4y: 1, 4, 16 Output

Write a program in C to find the value of 𝒙 for 𝒚 = 𝟗 using Inverse Interpolation from the data:x: 1, 2, 4y: 1, 4, 16 Output

Write a program in C to find 𝒚 at 𝒙 = 𝟏. 𝟓 using the Newton’s Forward Difference Method given data:x: 1, 2, 3, 4y: 1, 8, 27, 64 Output

Write a program in C to find 𝒚 at 𝒙 = 𝟒. 𝟓 using Newton’s Backward Difference Method with data:x: 1, 2, 3, 4, 5y: 1, 8, 27, 64, 125 Output

Write a program in C to find 𝒚 at 𝒙 = 𝟑 using Newton’s Divided Difference Method given data:x: 1, 2, 4y: 1, 4, 16 Output

Write a program in C to find the value of using the Trapezoidal Rule with 𝒏 = 4 Output

Write a program in C to find the value of using the Simpson’s 1/3 Rule with 𝒏 = 4 Output

Write a program in C to find the value of using the Simpson’s 3/8 Rule with 𝒏 = 4 Output

Write a program in C to solve the differential equation 𝒇𝒓𝒂𝒄𝒅𝒚𝒅𝒙 = 𝒙 + 𝒚 with 𝒚(𝟎) = 𝟏 at 𝒙 = 𝟎. 𝟏 using Euler’s Method. Output

Write a program in C to solve 𝒇𝒓𝒂𝒄𝒅𝒚𝒅𝒙 = 𝒙 + 𝒚 with 𝒚(𝟎) = 𝟏 at 𝒙 = 𝟎. 𝟏 using the Modified Euler’s Method. Output

(a) Runge–Kutta 2nd Order Write a program in C to solve 𝒇𝒓𝒂𝒄𝒅𝒚𝒅𝒙 = 𝒙 + 𝒚 with 𝒚 (𝟎) = 𝟏 at 𝒙 = 𝟎. 𝟏 using the Runge–Kutta 2nd Order Method. Output (b) Runge–Kutta 4th Order Write a program in C to solve 𝒇𝒓𝒂𝒄𝒅𝒚𝒅𝒙 = 𝒙 + 𝒚 with 𝒚 (𝟎) = 𝟏 at…