Numerical Methods (1)

Question 1

What if f(x) changes sign?

Answer 1

I know it has passed through a root

Question 2

I know it has passed through a root

Answer 2

What if f(x) changes sign?

Question 3

How to show a root lies in the interval between two values a and b?

Answer 3

Find f(a) and f(b)
Two answers have different signs and function is continuous over the interval

Question 4

Find f(a) and f(b)
Two answers have different signs and function is continuous over the interval

Answer 4

How to show a root lies in the interval between two values a and b?

Question 5

What is the same as x^3 - x^2?

Answer 5

(x^2)(x-1)

Question 6

(x^2)(x-1)

Answer 6

What is the same as x^3 - x^2?

Question 7

What is the newton-raphson method?

Answer 7

x_n+1 = x_n - f(x_n)/f’(x_n)

Question 8

x_n+1 = x_n - f(x_n)/f’(x_n)

Answer 8

What is the newton-raphson method?

Question 9

What are the convergent iterations graphs?

Answer 9

Convergent staircase diagram
Convergent cobweb diagram
Divergent staircase diagram

Question 10

Convergent staircase diagram
Convergent cobweb diagram
Divergent staircase diagram

Answer 10

What are the convergent iterations graphs?

Question 11

The approximation for concave curves?

Answer 11

Area is an underestimate

Question 12

Area is an underestimate

Answer 12

The approximation for concave curves?

Question 13

The approximation for convex curves?

Answer 13

Area is an overestimate

Question 14

Area is an overestimate

Answer 14

The approximation for convex curves?