Quantitative Methods Answers

Given f(0) = – 18, f(1) = 0, f(3) = 0, f(5) = – 248, f(6) = 0, f(9) = 13104; find f(x).

Certain corresponding values of x and log10x are given below:

x: 300 304 305 307

log10 x: 2.4771 2.4829 2.4843 2.4871

Find log10 (310) by Lagrange’s formula.

The following table gives the viscosity of an oil as a function of temperature. Use Lagrange’s formula to find the viscosity of oil at a temperature of 140°.

Temp° : 110 130 160 190

Viscosity: 10.8 8.1 5.5 4.8

Find the equation of the cubic curve that passes through the points (4, – 43), (7, 83), (9, 327) and (12, 1053).

Given the table of values

x: 50 52 54 56

3√x : 3.684 3.732 3.779 3.825

Use Lagrange’s formula to find x when 3√x = 3.756,

If y(1) = – 3, y(3) = 9, y(4) = 30, and y(6) = 132, find the four-point

Lagrange interpolation polynomial that takes the same values as the function y at the given points.

Given the table of values

x : 150 152 154 156

y = √x : 12.247 12.329 12.410 12.490

Evaluate √155 using Lagrange’s interpolation formula.

If y(1) = – 3, y(3) = 9, y(4) = 30, and y(6) = 132, find the four-point

Lagrange interpolation polynomial that takes the same values as the function y at the given points.

If y0, y1, ..., y9 are consecutive terms of a series, prove that

y5 = 1/70 [56(y4 + y6) – 28(y3 + y7) + 8(y2 + y8) – (y1 + y9)]

Find the value of tan 33° by Lagrange’s formula if

tan 30° = 0.5774, tan 32° = 0.6249,

tan 35° = 0.7002, tan 38° = 0.7813.