MatLAB Answers

Find the root of the polynomial given below within the interval (-1, 1) using (a) the bisection method and (b) the Newton’s method

P = x/8[(63x^4)-(70x^2)+15]

QI. Find the number n of distinct permutations that can be formed from all the letters of each word: (a) THOSE (b) UNUSUAL (c) SOCIOLOGICAL

The following table shows the acceleration (m/s2) of a vehicle over time. Calculate the velocity (m/s) and the displacement (m) of the vehicle at t=1, 2,….,10 s using trapezoidal rule.

Time (s) Acceleration (m/s2)

0 0

1 1

2 3

3 5

4 8

5 10

6 13

7 15

8 18

9 21

10 25

1. The change in the heat capacity of a substance due to temperature is given in the table below. Calculate the heat required to raise the temperature of 1-mole of the substance from 300 K to 1000 K using (a) Trapezoidal rule and (b) Simpson’s rule.

(Hint: )

T (K) / C_p (Cal/mol.K)

300 19.65

400 26.74

500 32.80

600 37.74

700 41.75

800 45.6

900 47.83

1000 50.16

1. Integrate the function below between the limits 0 and 0.8 by (a) Trapezoidal rule and (b) Simpson’s rule.

Find the root of the following equation using the Newton-Raphson method. Choose the initial guess as x(0) = 10. Choose the error tolerance as tol=1e-6. In other words, the iterations should be stopped when the error

|x(1) − x(i-¹)| ≤ tol.

x^2.5 23x^1.5 - 50x + 1150 = 0

i. Please report the value of x after 2 iterations

ii. Please report the converged solution, where error is less than 1e-6.

iii. Please report the number of iterations required to reach this converged solution.

Find the root of the following equation using the Newton-Raphson method. Choose the initial guess as x(0) = 10. Choose the error tolerance as tol=1e-6. In other words, the iterations should be stopped when the error

|x(1) − x(i-¹)| ≤ tol.

x^2.5 23x^1.5 - 50x + 1150 = 0

Find the root of the following equation using the Newton-Raphson method. Choose the initial guess as 𝑥 (0) = 10. Choose the error tolerance as tol=1e-6. In other words, the iterations should be stopped when the error i. Please report the value of x after 2 iterations ii. Please report the converged solution, where error is less than 1e-6. iii. Please report the number of iterations required to reach this converged solution

Find the root of the following equation using the Newton-Raphson method. Choose the

initial guess as 𝑥

(0) = 10. Choose the error tolerance as tol=1e-6. In other words, the

iterations should be stopped when the error

i. Please report the value of x after 2 iterations

ii. Please report the converged solution, where error is less than 1e-6.

iii. Please report the number of iterations required to reach this converged solution

Write a MATLAB program to solve the following two-point boundary

value problem for

d^2theta/dt^2 = -theta(t); 0 < t < 2theta; theta(0) = 0.7; theta(2pie) = 0.7:

Find the solution of the given equation using the Trapezoidal rule:

int(5, - 2) sqrt(x^2+1)

Take the number of intervals to be 10.