In each of 9 and 10, let 0(t) = 0 and use the method of successive approximationsto approximate the solution of the given initial value problem.(a) Calculate 1(t), ... , 3(t).(b) Plot 1(t), ... , 3(t) and observe whether the iterates appear to be converging.y= t2 + y2, y(0) = 0

S343 Section 2.7 Notes- Euler’s Method of Numerical Approximation 9-13-16 Used for equations that cannot be solved without computer- give numerical approximation of at given values Known as first-order method/tangent line method- error at each step (iteration) decreases like ℎ decreases +ℎ − ) Recall = (, )) = ℎ→0 ( ℎ ) where ℎ = uniform step size between and +1 (ie. = + ℎ) +1 +ℎ −() o (, )) ≈ ℎ ℎ( (, ))≈ + ℎ − ( )