Use the newton-raphson method to find the root of the equation f(x) = in(3x) + 5x2, using an initial guess of x = 0.5 and a stopping criterion of & = 0.1%. report your answer to 3 decimal places. what is the estimate for the root? what is the approximate relative error? %

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

 f(x)=log (3 x) +5 x²

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

So, root of the equation =0.205 (Approx)

Approximate relative error

 Approximate relative error in terms of Percentage

   =0.41 × 100

   = 41 %

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form