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X —> 1 5 9 13 17
y = f(x) —> 13 16 18 21 26
Hence construct the interpolating polynomial that uses all this data. Also find f[15x0.(i+2)]. where i=2
A pulley (A) diameter 300m is accelerated by means of a belt drive from 60rpm to 240rpm during 360 revolutions. Attached by means of a belt is another pulley (B) with diameter 200mm. Calculate
a) the angular acceleration of each pulley
b) the initial and final velocity of the smaller pulley (B) in rad/s
X —> 1 3 5 6
y=f(x) —> -12 -14 -20 -20
For the following voltage function, find the numerical differentiation of first order using the finite divided-difference formula at a point, 1, - 4.5 s with step forward, backward and center finite divide-difference formula at a point t1=4.5 s with step size, h=0.i s, where i=72
v(t) = 20sint-t^3/18
Evaluate the values using the conventional differentiation formula aiso and hence comment which numerical method produce better result based on the percentage of true error.
For the following function, find the numerical differentiation of first order using forward, backward and center finite divided-difference formula at a point, 1, =3.2s with step size, h =0.i s, where i= 72,
i(r) = 40sint -10t^2
Evaluate the values using the conventional differentiation formula also and hence comment which numerical method produce better result based on the percentage of true error.
Evaluate f(N)=3√N, N=72, to five decimal places by Newton-Raphson iterative method.
Determine a real root accurate to four decimal places of the following equation by using (i) Bisection Method (ii) Fixed Point Iteration Method (iii) Method of False Position and (iv) Newton-Raphson.
16-9(x - sin x) = 0; interval [2, 3]
Question 1 With reference to Table 1 below, list quantities of electrical, magnetic and capacitive circuits which are analogous to the given ones. (One mark each) Electric circuits Magnetic Circuits Capacitive Circuits 8.1……………. Magnetic Flux 8.2 …………… 8.3 …………… 8.4 …………… e.m.f Potential difference 8.5 …………… 8.6 …………… 8.7 …………… 8.8 …………… Electric flux density 8.9 …………… 8.10 …………… Permittivity
Evaluate ∫y=0^{1}∫x=y^{√2-y^{2}}y/√x^{2}+y^{2}dxdy ,by clange the order of integration.
Question 1 With reference to Table 1 below, list quantities of electrical, magnetic and capacitive circuits which are analogous to the given ones. (One mark each) Electric circuits Magnetic Circuits Capacitive Circuits 8.1……………. Magnetic Flux 8.2 …………… 8.3 …………… 8.4 …………… e.m.f Potential difference 8.5 …………… 8.6 …………… 8.7 …………… 8.8 …………… Electric flux density 8.9 …………… 8.10 …………… Permittivity
