Question

Using bisection method the root e^x-3x=0,correct to two decimal places,which like between 1 and 2 is A)1.51 B)1.52 C)1.6 D)1.55

Answer 1

Answer:

aiflsuspd 0ueudihhhhuu

Answer 2

Answer:

Using bisection method, the root of e^x-3x=0,correct to two decimal places,between 1 and 2 is 1.51.

Option (A) 1.51 is the right answer.

Step-by-step explanation:

• Numerical methods in mathematics use numerical approximations for solving complex mathematical problems that usually has no analytical solution.

• They follow algorithms (series of steps) to arrive at a solution.

There are several types of numerical methods such as:

1. Euler method
2. Trapezoidal law
3. Range - Kutta methods
4. Newton method

What is Bisection method?

Bisection method is the most straight forward numerical method to solve a polynomial equation or a continuous function.

Method:

1. Initially by trial and error method, find two numbers (a,b) such that the function is positive at one number (b) and negative at the other (a).
2. Then calculate the average of the two numbers (m = (a+b)/2).
3. Repeat the first step with two numbers and the average.
4. If the function value is positive at m and negative at a then the new set of numbers become (a,m).
5. If the function value is negative at m and positive at b then the new set of numbers become (m,b).
6. If the function value is zero at m, them m is the root of the equation or function.
7. Repeat this procedure until the function value approaches zero.

Calculation:

Given equation is f(x) =  $e^{x} -3x = 0$

And the interval is [1,2]

f(1) = e - 3 = 2.718 - 3 = -0.282

f(2) = $e^{2} - 6$ = 1.389

Since f(1) is negative and f(2) is positive, there exists a root in this interval.

m = average of 1,2 = (1 + 2) / 2 = 1.5

f(1.5) = $e^{1.5} -3*1.5 = -0.0183$

Since f(1.5) is negative and f(2) is positive, there exists a root in this interval.

m = average of 1.5, 2 = (1.5+2)/2 = 1.75

f(1.75) = $e^{1.75} -3*1.75 = 0.504$

Since f(1.5) is negative and f(1.75) is positive, there exists a root in this interval.

m = average of 1.5,1.75 = (1.5 + 1.75) / 2 = 1.625

f(1.625) = $e^{1.625} -3*1.625 = 0.203$

Since f(1.5) is negative and f(1.625) is positive, there exists a root in this interval.

f(1.56) = $e^{1.56} -3*1.56 = 0.083$

Since f(1.5) is negative and f(1.56) is positive, there exists a root in this interval.

m = average of 1.5,1.56 = (1.5+1.56)/2 = 1.53

f(1.53) = $e^{1.53} -3*1.53 = 0.03$

Since f(1.5) is negative and f(1.53) is positive, there exists a root in this interval.

m = average of 1.5,1.53 = (1.5+1.53)/2 = 1.506

f(1.506) = $e^{1.506} -3*1.506 = -0.008$

Since f(1.506) is negative and f(1.53) is positive, there exists a root in this interval.

m = average of 1.506,1.53 = (1.506+1.53)/2 = 1.518

f(1.518) = $e^{1.518} -3*1.518 = 0.009$

Since f(1.506) is negative and f(1.518) is positive, there exists a root in this interval.

m = average of 1.506,1.518 = (1.506+1.518)/2 = 1.512

f(1.512) = $e^{1.512} -3*1.512 = -0.0002$

Since f(1.512) is negative and f(1.518) is positive, there exists a root in this interval.

Therefore the root of $e^{x} -3x = 0$ between 1 and 2 correct to two decimal places is 1.51.

Option (A) 1.51 is the right answer.

Find more similar problems on numerical methods:

https://brainly.in/question/7485698

When do we need to use a numerical method instead of analytical method for integration?

https://brainly.in/question/44088797