Numerical Differentiation

Question 1

What is the formula for Forward’s difference approximation formula?

Answer 1

f’(c) = f(c + h) -f(c) / h

As ‘h’ tends to 0

Question 2

What is the formula for Central Difference Approximation Formula?

Answer 2

f’(c) = f(c + h) - f(c - h) / 2h

As ‘h’ tends to 0

Question 3

What are the two ways of numerical integration approximation?

Answer 3

Forward Difference Approximation
Central Difference Approximation

Question 4

What is the relationship between value of ‘h’ and approximation?

Answer 4

A smaller value of ‘h’ gives a better approximation

Question 5

Which approximation is better?

Answer 5

For most polynomials, central difference is better than forward

Question 6

How do inaccuracies arise from the approximation?

Answer 6

Inaccuracies can result from the level of a computer’s precision which leads to loss of significant figures in calculation

Question 7

What is the formula for the error between ‘X’ and ‘x’?

Answer 7

If(X) - f(x)I = I(X - x)I * f’(x)

X is the exact value
x is the approximation