non matlab solution please dynamic viscosity of water 103 n sm2 is related to temperature tc in

(b) To use linear interpolation to predict μ at T = 7.5 °C, we need to find the two data points

Non matlab solution please dynamic viscosity of water 103 n...

Dynamic viscosity of water μ (10–3 N · s/m2) is related to temperature T (°C) in the following manner: T 0 5 10 20 30 40 μ 1.787 1.519 1.307 1.002 0.7975 0.6529 (b) Use linear interpolation to predict μ at T = 7.5 °C. (c) Use polynomial regression to fit a parabola to the data in order to make the same prediction.

Transcript

00:01 Hello everyone, so in this question, the a part if we apply the taylor's theorem, right, for writing the degree for polynomial centered, we will get like this.

00:22 F of x is equal to f of 0 plus x f -f dash of 0 plus x squared by 2 f -dash -dash of 0 plus x squared by 2 f -dash -dash of 0 plus x cube by 3.

00:42 Bq plus x par 4 by 4 q right now applying the newton 11x formula for the derivative of definite integral f of x is equal to minus 1 plus integral of g of t d t from 0 to 2x now if we find out f of 0 0 0 0 0.

01:24 That would be minus 1 plus 0 which is minus 1 and f dash of x would be b by d x of 2x into g of 2x right so uh using the info x n dash is equal to n x in power n minus 1 now f dash of 0 would be 2g of 0 which is 2g of 0 which is 1 by 2.

02:06 In this way f double dash 0 is equal to 4 g dash of 2x at x is equal to 0 that would be minus 1 by 2 and f dash dash dash of 0 is equal to 8 g dash of 2x at x is equal to 0 and this would be 3 by 4 and the final integral derivative would be 16 of 2x at x is equal to 0 and this is minus 3 by 2.

02:56 Since we have all the values, now if we plug the series here, p4 of x is equals to minus 1 plus x by 2 minus x square by 4 plus 3x cube by 24, minus 3x cubed by 24, minus 3x.

03:17 X par 4 by 48.

03:21 This is the series? now this is the a part.

03:26 Now in the b part if we find out the general term, right, that would be p4 of x is equal to minus 1 plus x by 2 minus x squared by 4 plus x cubed by 8 minus x par 4 by 16 and the general term a n is equal to minus 1 power n into x by 2 whole power n minus 1.

04:11 This is the general down.

04:13 So this is the b part and in the c part the interval of convergence by ratio test that would be limit of n tends to infinity, a.

04:29 N minus 1 by a .n...

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