Posted by **farouk** on Tuesday, November 15, 2011 at 3:53pm.

Show that the equation x+3sinx=2 has a root between 0.4 and 0.6.express the root to four significant figures

- calculus -
**MathMate**, Tuesday, November 15, 2011 at 4:43pm
First part:

let

f(x)=x+3sin(x)-2

f(0.4)=-0.432

f(0.6)=0.294

By the intermediate value theorem for a continuous function, there must be a value of x=x0 between 0.4 and 0.6 such that f(0.4)≤f(x0)≤f(0.6), specifically where f(x0)=0.0.

There are many ways to find the root of f(x)=0, for example, arrange the equation as:

x=arcsin((2-x0)/3)

and iterate starting with x0=0.5

then x=arcsin((2-0.5)/3)=0.5236

Let x0=0.5236 and continue until the value is stable.

Alternatively, use Newton's method for the iteration:

x1=x0-(x0+3sin(x0)-2)/(1+3cos(x0))

Starting from x0=0.5, you will get 9 digits of accuracy with 2 iterations.

## Answer This Question

## Related Questions

- calculus - Show that the equation;x+3sinx=2 has a root between x=0.4 and x=0.6 ...
- calculus - Use Newton's method to approximate the indicated root of the equation...
- Pre-Calculus - Solve. Express your answer as exact roots. (s+6)^2 = 3/4 Sq root...
- Pre-Calculus - Solve 0 = 3x^2 + 5x -1 by completing the square. Express your ...
- Algebra - I had to solve 2x^2-x-1 using the quad. formula. I got it down to (1...
- Trig. - 2sin^2x-3sinx=-1 sin^2x-3sinx=-1/2 times -3 sq. root of (sin^2x)+sinx= ...
- math - Four students work to find an estimate for square root 37. Who is closest...
- Math - Four students work to find an estimate for square root 27. Who is closest...
- math - Four students work to find an estimate for square root 54. Who is closest...
- maths surds please help and explain - Simplify A.1/root a +2 b.root 18/25 c.root...

More Related Questions