Submit both the Matlab code and results for the following questions Q1 Use Matla

Question

Submit both the Matlab code and results for the following questions Q1 Use Matlab program to obtain fourth-order Taylor series expansions to predict 10.5) for,f(x) = ln x using a base point at x = 1 Q2 Maming' formula for arectangular channel can be wntten as 1 (BH)5/3 n (B +2H)2/3 VS where Q = flow (m3/s), n = a roughness coefficient, B width (m), H= depth (m), and S= slope You are applying this formula to a stream where you know that the vhdth = 20 m and the depth 0.3 m. Unfortunately, you know the roughness and the slope to only a ± 10% precision. That is, you know that the roughness is about 0.03 with a range from 0.027 to 0.033 and the slope is 0.0003 with a range from 0.00027 to 0.00033. Use a first-order error analysis to determine the sensitivity of the flow prediction to each of these two factors i.e. n and S) Help you can write matlab expression as follows Expression Matlab format 3/2 Q.3 , The deflection y of the top of a sailboat mast is expressed as: FL SEI where r 50 ± 2 (lb / ft) = side loading = L= height 30±0.1 (M) = 1 ,5 x10s ± 0.01 x10s (lb / ft*) 0.06± 0.0006 (fr) E = modulus of elasticity = 1 = moment of inertia a) Estimate the error in y due to uncertainty in the variables. b) Check whether a first order estimate of Taylor series is valid for your calculations

Explanation / Answer

Q1

code

clear
clc

syms x;
result(x) = taylor(log(x), x, 'ExpansionPoint', 1, 'Order', 4);
result
result_value = result(2.5);
result_value

output

result(x) =
x - (x - 1)^2/2 + (x - 1)^3/3 - 1
result_value =
3/2

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