Question

The slope (????) of the beam is given by:

θ(x) = dy/dx

Required:
Use a forward divided difference and a step size of h=0.3 to approximate the slope of the beam at x = 1. Calculated the true percent relative error.

Answer 1

Explanation:

From the given question:

The slope is expressed as;

`\thteta (x) = (dy)/(dx) - - (1)`

`\thteta (x) = (dy)/(dx)\left \{ {{(y(x+b)-y(x))/(h) \ \ \to approximate} \atop {(1)/(100)}(-4+4x-3x^2+2x^3) \ \to \ exact } \right.`

∴

`\theta (x) _(approximate) = (y(1+0.3)-y(1))/(0.3)`

`\theta (x) _(approximate) = (y(1.3)-y(1))/(0.3)`

`\theta (x) _(approximate) = -2.965 * 10^(-5)`

`\theta(x)_(exact) = (1)/(100)(-4+4-3+2)`

`\theta(x)_(exact) = -0.01`

Finally, the true percent relative error TPRE is:

`TPRE= ( | \theta(x)_(approximate) -\theta (x)_(exact) )/(\theta (x)_(exact) )* 100\%`

`TPRE= ( 2.965 * 10^5 --0.01)/(-0.01)* 100\%`

TPRE = 70..35%