Suppose f′(x) = x√sin (x^2) and f(0) = 5. Estimate f(b) for:

Question

Suppose f′(x) = x√sin (x²) and f(0) = 5.

Estimate f(b) for:

b = 0 : f(b) ≈

b = 1: f(b) ≈

b = 2 : f(b) ≈

b = 3 : f(b) ≈

Answer 1

deltaX = 50 , that is each interval (0,1) , (1,2),(2,3)

is divided in to 50 pieces

Runge Kutta says:

b=0 ->5.32148881679566686

b=1.76 ---> 6.19506194120141065

b = sqrt(pi) ---> 6.19785486401622351

the function does not exist on parts of this interval...

sin t > 0, for t = 0..pi

0 < t < pi

0 < x^2 < pi

0 < x < sqrt(pi) = 1.7724538509055160272981674833411

Runge Kutta calculator used at Keisan Casio dot com