Tiêu đề Test 21 - Related Rates, Euler's Method, Slope Fields solutions_vF.pdf ✅

Test 21 - Related Rates, Euler’s Method and Slope Fields Substitute d y d x = k y into the equation, then run the iterations until n = m. yn+1 = yn +h ·(k y) ̄ ̄ ̄ x=xn,y=yn yn+1 = yn +hk yn y1 = y0(1+hk) y2 = y1(1+hk) y3 = y2(1+hk) y4 = y3(1+hk) . . . ym = ym−1(1+hk) Substitute y1 into the expression for y2, y2 into the expression for y3, and so on, until ym−1 gets substituted into the expression for ym. ym = y0 (1+hk)×(1+hk)×(1+hk)×··· ×(1+hk) | {z } m times = y0(1+hk) m = A(1+hk) m The correct answer is D . (c) Let the step size be 1 2 and the initial value be 3. If the value of k is 2, find the number of iterations needed for an approximated value to reach 12. [1 mark] A. 1 B. 3 C. 2 D. 4 E. 5 Specialist Maths 3/4 © EdAtlas | Page 4 © EdAtlas