Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 12 TN Board chapter 5 - Numerical Methods [Latest edition]

Evaluate Δ(log ax)

If y = x³ – x² + x – 1 calculate the values of y for x = 0, 1, 2, 3, 4, 5 and form the forward differences table

If h = 1 then prove that (E^–1Δ)x³ = 3x² – 3x + 1

If f(x) = x² + 3x than show that Δf(x) = 2x + 4

Evaluate Δ`[1/((x + 1)(x + 2))]` by taking ‘1’ as the interval of differencing

Find the missing entry in the following table

Following are the population of a district

Find the population of the year 1911

Find the missing entries from the following.

Using graphic method, find the value of y when x = 48 from the following data:

The following data relates to indirect labour expenses and the level of output

Estimate the expenses at a level of output of 350 units, by using graphic method.

Using Newton’s forward interpolation formula find the cubic polynomial.

The population of a city in a censes taken once in 10 years is given below. Estimate the population in the year 1955.

In an examination the number of candidates who secured marks between certain intervals was as follows:

Estimate the number of candidates whose marks are less than 70.

Find the value of f(x) when x = 32 from the following table:

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy.

Find the melting point of the alloy containing 84 percent lead.

Find f(2.8) from the following table:

Using interpolation estimate the output of a factory in 1986 from the following data.

Use Lagrange’s formula and estimate from the following data the number of workers getting income not exceeding Rs. 26 per month.

Using interpolation estimate the business done in 1985 from the following data

Using interpolation, find the value of f(x) when x = 15

Choose the correct alternative:

Δ²y₀ = 

Choose the correct alternative:

Δf(x) =

Choose the correct alternative:

E ≡

Choose the correct alternative:

If h = 1, then Δ(x²) = 

Choose the correct alternative:

If c is a constant then Δc =

Choose the correct alternative:

If m and n are positive integers then Δ^m Δⁿ f(x)=

Choose the correct alternative:

If ‘n’ is a positive integer Δⁿ[Δ^-n f(x)]

Choose the correct alternative:

E f(x) =

Choose the correct alternative:

∇ ≡

Choose the correct alternative:

∇f(a) =

Choose the correct alternative:

For the given points (x₀, y₀) and (x₁, y₁) the Lagrange’s formula is

Choose the correct alternative:

Lagrange’s interpolation formula can be used for

Choose the correct alternative:

If f(x) = x² + 2x + 2 and the interval of differencing is unity then Δf(x)

Choose the correct alternative:

For the given data find the value of Δ³y₀ is

If f(x) = e^ax then show that f(0), Δf(0), Δ²f(0) are in G.P

Prove that (1 + Δ)(1 – ∇) = 1

Prove that  Δ∇ = Δ – ∇

Prove that EV = Δ = ∇E

A second degree polynomial passes though the point (1, –1) (2, –1) (3, 1) (4, 5). Find the polynomial

Find the missing figures in the following table:

Find f(0.5) if f(– 1) = 202, f(0) = 175, f(1) = 82 and f(2) = 55

From the following data find y at x = 43 and x = 84.

The area A of circle of diameter ‘d’ is given for the following values

Find the approximate values for the areas of circles of diameter 82 and 91 respectively

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃ = 465

From the following table obtain a polynomial of degree y in x.

Using Lagrange’s interpolation formula find a polynominal which passes through the points (0, –12), (1, 0), (3, 6) and (4, 12)