Question

8. Use the differential to approximate each quantity. (a) 0.99 (b) 145 (c) 20.01

Answer 1

8 a set fra)=ra f'(a)= 2x Then by the detination flaton) - fea) = f'(2) 42 or flatan)= feng + t'(a) an 0 have to find the value forgg Man we row we take 25 0.9 on=0.09 Then x0.09 roog + 200 g 0.99 0.948683 + Xo.09 2 x 0.9 0.99612 (round upto five decimal places) Therefore the approximate value is 0.99612 70.99 We have to find the value √145 det x=144 42=1 1 21194 Therefore from above eqr @) we get ✓145 = √144 + = 12 + 24 = 12.0417 (round up to four decimal places, Therefore r195a 12.0417 (approx)

(C) Let tead=ee f'(a)=.ee row by the debination fraroa) f(a) = f'(a) dx a f(a+09) = f(a) + f'(926x 0.01 e we Shall find the value and 02 = 0.01 So we take 2= 0 all these value putting 0.01 e e te.10.01) = 1+ (0.01)*1 = 1 + 0.01 = 1:01 1:01 There fore the approximate value of pool is