need 4,5 For equation v = e^2x + 4 = 0.5 Solve using incremental search with x_o

Question

need 4,5

For equation v = e^2x + 4 = 0.5 Solve using incremental search with x_o = -4 and delta x = 1. Solve using bisection method starting out with x_L = -5 and x_R = 5. Solve using Newton-Rhapson method with initial x_i = -6. Solve using secant method with initial x_i = and x_i + 1 = 8. What is the dependent and independent variable for this equation? How would the equation look like if you switched the independent and dependent variables around? All five problems have equal weight. Problems 1-4 should all produce the same solution. However, all relevant steps will need to be shown for each problem's solution in order for credit to be given.

Explanation / Answer

4.

f= e2x+4-0.5

x0= -5

f0 = e2*-5 +4-0.5

=e-6-0.5

=-0.4975212

Now x1= -4

f1=e-2*4+4-0.5

f1=e-4-0.5

=-0.481684

Secant formula = x2= f1x0-f0x1/(f1-f0)

x2 =-0.481684*(-5) –(-0.4975212*-4)/(-0.481684 –(-0.4975212)) =26.4147

Similarly we can proceed by finding x3 =f2x1-f1x2/(f2-f1)

And can find x4,x5,x6 and so on till two consecutive roots becomes nearly equal .

5.

The independent variable is ‘x’ and dependent variable is ‘v’.If we switch them around the equation would look like x = e2v +4 -0.5

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