Quantitative Methods Answers

if "f(3)" =5 and "f(5)" =3, what is the form of "f(x)" by lagrange's formula

Perform three iteration of the bisection method compute the positive root of

the equation f(x) = x² – 5x + 2

Find a root of the following equations correct to three decimals using Newton's raphson method: x³ -5x +3=0

Use simpson's method to approximate

8

∫ (x^2-x+3)dx with 8 sub-interval

Use the Newton’s method to approximate the real solution of xcube-2x-2=0 in the interval [1,2]

Find the negative root of the equation x^3 - 2x + 5 =0

Find the real roots of the equation x^3 + x^2 - 100= 0 by the iteration method

The force F on a beam of length 5m is given by

𝐹= ∫⁵₀ 𝑒𝑥/1+ √𝑥

Find the value of F using the trapezium rule, Simpsons rule and the mid ordinate rule with a suitable number of intervals.

4. The equation for the velocity of a car is given as

Y = √𝑥 + 1𝑥

Use the trapezium rule, Simpson’s rule and the mid ordinate rule ( with a suitable number of intervals ) to find the distance travelled between 1 and 6 seconds.

Compare your answers to the value given by the definite integral and comment on the accuracy of the numerical methods.