Find the polynomial value

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Reference no: EM133067576

Question 1. The table below gives the temperatures T(OC) and lengths(mm) of a heated rod. If l = a₀ + a₁T, find the values of a₀ and a₁ using linear least squares. Find the length of the rod when T = 72.5°C.

T	40	50	60	70	80
l	600.5	600.6	600.8	600.9	601.0

Question 2. The temperature of a metal strip was measured at various time intervals during heating and the values are given in the table below.

Time('t' min)	1	2	3	4
Temp('T' OC)	70	83	100	124

If the relation between the time ‘t' and temperature ‘T' is of the form: T = be^t/4 + a. Estimate the temperature at t = 6 minute.

Question 3. Fit a second order polynomial to the data given in the table below.

x	1	2.1	3.2	4
f(x)	2	2.5	3.0	4

Find the polynomial value at 1.5 and 3.8.

Question 4. Given the table of values

x	5	4	3	2	1
z	3	-2	-1	4	0
y	15	8	-1	26	8

Use multiple linear regression formula to fit the data of the form: y = a₁ + a₂(x) +a₃(z) & Find f(5.3) and f(3.7).

Question 5. Fit a natural cubic B-Spline, S to the data given below in the table.

x	1.2	2.8	3.5	4.1	5.9
f(x)=x3-1	-2	-1	0	1	2

Find the functional value at 1.5 and 6

Reference no: EM133067576

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