8. Find the positive root of the equation 3x - cos x - 1 using Regula Falsi method and correct upto 4c) 0.6071 d) 0.5701decimal places. a) 0.6701b) 0.50719. Find the positive root of the equation x³ + 2x² + 10x - 20 using Regula Falsi method and correct upto 4decimal places. a) 1.3688b) 1.3866c) 1.4688d) 1.648810. Find the positive root of the equation 3x + sin x - e* using Regula Falsi method and correct upto 4b) 0.4306c) 0.3604d) 0.4304decimal places a) 0.460411. Rate of convergence of the Newton-Raphson method is generallya) Linearb) Quadraticc) Super-lineard) CubicESTD: 2001RNS INSTITUTE OF TECHNOLOGY, BENGALURU - 98DEPARTMENT OF MATHEMATICS12. The Newton-Raphson method of finding roots of nonlinear equations falls under the category of whichof the following methods? a) bracketingb) open c) random d) graphical13. The Newton Raphson method is also called asa) Tangent method14. The Iterative formula for Newton Raphson method is given bya) Xn+1 = xob) Xn+1 = xnf(xn)f1(xn)c) Xn = xof(xn)f'(xn)15. In Newton Raphson method f'(x) for a given point is given by the formulaa) y/x'b) y'/xc) y/xd) y' /x'16. In Newton Raphson method if the curve f(x) is constant thenb) f(x) = 0c) f'(x) = 0d) f'(x) = ca) f'(x) = 017. For decreasing the number of iterations in Newton Raphson method:a) The value of f'(x) must be increased b) The value of f"(x) must be decreasedc) The value of f'(x) must be decreased d) The value of f"(x) must be increased18. The equation f(x) is given as x³ - x² + 4x -4 = 0. Considering the initial approximation at x=2 then thevalue of next approximation correct upto 2 decimal places is given asa) 0.67b) 1.33c) 1.00d) 1.5019. The equation f(x) is given as x²-4=0. taking the initial approximation at x=6 then the value of nextapproximation correct to 2 decimal places is given as a) 3.33 b) 1.33 c) 2.33 d) 4.3320. The equation f(x) is given as x³+4x+1=0. Considering the initial approximation at x=1 then the valueof x₁ is given as a) 1.67c) 1.86d) 1.85b) 1.8721. At which point the iterations in the Newton Raphson method are stopped?a) When the consecutive iterative values of x are not equalb) When the consecutive iterative values of x differ by 2 decimal placesc) When the consecutive iterative values of x differ by 3 decimal placesd) When the consecutive iterative values of x are equal22. The Newton Raphson method fails ifa) f'(x) = 0 b) f"(x) = 0c) f(x) = 023. The points where the Newton Raphson method fails are called?b) continuousa) floatingf(xn)f'(xn)b) Secant method c) Chord methodd) Diameter methodd) Xn+1 = xn +d) f'(x) = 0c) non-stationary d) stationary24. Newton- Gregory Forward interpolation formula can be useda) only for equally spaced intervals b) only for unequally spaced intervalsc) for both equally and unequally spaced intervals d) for unequally intervalsX:f(x):RNS INSTITUTE OF TECHNOLOGY, BENGALURU - 98DEPARTMENT OF MATHEMATICSESTO 2001An Pustitute with Difference25. Newton- Gregory backward interpolation formula can be useda) only for equally spaced intervals b) only for unequally spaced intervalsc) for both equally and unequally spaced intervals d) for unequally intervals26. The following x,y data is given. The Newton's divided difference second order polynomial for theabove data is given by f₂(x)=b+b₁(x-15)+b₂(x-15)(x-18)f(xn)f'(xn)1524d) 24.00018 2237 25The value of b, is most nearlyb) 0.14333c) 4.3333a) 1.048027. The following data of the velocity of a body is given as a function of time.Time (s)0 15 18 22 24Velocity (m/s) 22 24 37 25 123If you were going to use quadratic interpolation to find the value of the velocity at t = 14.9 seconds,what three data points of time would you choose for interpolation?

Question

8. Find the positive root of the equation 3x - cos x - 1 using Regula Falsi method and correct upto 4c) 0.6071 d) 0.5701decimal places. a) 0.6701b) 0.50719. Find the positive root of the equation x³ + 2x² + 10x - 20 using Regula Falsi method and correct upto 4decimal places. a) 1.3688b) 1.3866c) 1.4688d) 1.648810. Find the positive root of the equation 3x + sin x - e* using Regula Falsi method and correct upto 4b) 0.4306c) 0.3604d) 0.4304decimal places a) 0.460411. Rate of convergence of the Newton-Raphson method is generallya) Linearb) Quadraticc) Super-lineard) CubicESTD: 2001RNS INSTITUTE OF TECHNOLOGY, BENGALURU - 98DEPARTMENT OF MATHEMATICS12. The Newton-Raphson method of finding roots of nonlinear equations falls under the category of whichof the following methods? a) bracketingb) open c) random d) graphical13. The Newton Raphson method is also called asa) Tangent method14. The Iterative formula for Newton Raphson method is given bya) Xn+1 = xob) Xn+1 = xnf(xn)f1(xn)c) Xn = xof(xn)f'(xn)15. In Newton Raphson method f'(x) for a given point is given by the formulaa) y/x'b) y'/xc) y/xd) y' /x'16. In Newton Raphson method if the curve f(x) is constant thenb) f(x) = 0c) f'(x) = 0d) f'(x) = ca) f'(x) = 017. For decreasing the number of iterations in Newton Raphson method:a) The value of f'(x) must be increased b) The value of f&#34;(x) must be decreasedc) The value of f'(x) must be decreased d) The value of f&#34;(x) must be increased18. The equation f(x) is given as x³ - x² + 4x -4 = 0. Considering the initial approximation at x=2 then thevalue of next approximation correct upto 2 decimal places is given asa) 0.67b) 1.33c) 1.00d) 1.5019. The equation f(x) is given as x²-4=0. taking the initial approximation at x=6 then the value of nextapproximation correct to 2 decimal places is given as a) 3.33 b) 1.33 c) 2.33 d) 4.3320. The equation f(x) is given as x³+4x+1=0. Considering the initial approximation at x=1 then the valueof x₁ is given as a) 1.67c) 1.86d) 1.85b) 1.8721. At which point the iterations in the Newton Raphson method are stopped?a) When the consecutive iterative values of x are not equalb) When the consecutive iterative values of x differ by 2 decimal placesc) When the consecutive iterative values of x differ by 3 decimal placesd) When the consecutive iterative values of x are equal22. The Newton Raphson method fails ifa) f'(x) = 0 b) f&#34;(x) = 0c) f(x) = 023. The points where the Newton Raphson method fails are called?b) continuousa) floatingf(xn)f'(xn)b) Secant method c) Chord methodd) Diameter methodd) Xn+1 = xn +d) f'(x) = 0c) non-stationary d) stationary24. Newton- Gregory Forward interpolation formula can be useda) only for equally spaced intervals b) only for unequally spaced intervalsc) for both equally and unequally spaced intervals d) for unequally intervalsX:f(x):RNS INSTITUTE OF TECHNOLOGY, BENGALURU - 98DEPARTMENT OF MATHEMATICSESTO 2001An Pustitute with Difference25. Newton- Gregory backward interpolation formula can be useda) only for equally spaced intervals b) only for unequally spaced intervalsc) for both equally and unequally spaced intervals d) for unequally intervals26. The following x,y data is given. The Newton's divided difference second order polynomial for theabove data is given by f₂(x)=b+b₁(x-15)+b₂(x-15)(x-18)f(xn)f'(xn)1524d) 24.00018 2237 25The value of b, is most nearlyb) 0.14333c) 4.3333a) 1.048027. The following data of the velocity of a body is given as a function of time.Time (s)0 15 18 22 24Velocity (m/s) 22 24 37 25 123If you were going to use quadratic interpolation to find the value of the velocity at t = 14.9 seconds,what three data points of time would you choose for interpolation?

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