Question

(10 Marks) a. Evaluate the following limit using L'Hopital's Rule: lim In(cos(y)) y→0 Zy2 b. Ahmed got a car loan from the Bank Muscat and he repaid (Z * 250) OMR by making 'n' equal monthly payments of 250 OMR since he received the loan amount. If the rate of interest per month is 'r', this can be represented as, 1 50(1- (Z * 250r = 250 (1 (1+r)n) If n = 60 months, using Newton-Raphson method, find the rate of interest per month, (r) correct to 4 decimal places. Consider, ro = 0.05. (15 Marks)

note:

Z=10

Answer 1

answer :
S's las lim yo In clos (y)) 24² Since it form the o format therefore we apply which we differentiate both 2'Hopital rule, Numerator with respect to y. & denominator we get > lim lim .(Siny) & In close cosy Z.24 - (24²) dy limsing 9-90 } sing y lim acosys 2x1 Since z=6 therefore limit is - tugh) (b) let (8) - (Z+250)r - 250 (1. . 2567-250+ 250 (140) to) 256 + 250 (-14) (118gn+T

nif'co) = 256 2500 (14rnt! f(8) = 2568 - 250 + 250 Go (148) f'cona 256- (S000 - 250 250 Go (1+0.05) lo -0.05 fero): 256X0.05 13.00 15,000 flcro)=256- (1+0.05961 508.79 3196 f(ro) 4 = do 0.05. 13.00 508.793196 0.024449.