3.7.2 Numerical methods (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Question 16

$12\ln(x) - x^2 + 5 \quad x > 0$

a.

Show that $y = f (x)$ has a stationary point in the interval $[2.4, 2.5]$

[5]

b.

Starting with $x_0 = 2.45$ , apply the Newton-Raphson procedure twice to find an approximation for the $x\,$ coordinate of the stationary point in the interval $[2.4, 2.5]$ . Give your answer to 3 decimal places.

[4]

3.7.2 Numerical methods (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

Question 16

$12\ln(x) - x^2 + 5 \quad x > 0$

a.

Show that $y = f (x)$ has a stationary point in the interval $[2.4, 2.5]$

[5]

b.

Starting with $x_0 = 2.45$ , apply the Newton-Raphson procedure twice to find an approximation for the $x\,$ coordinate of the stationary point in the interval $[2.4, 2.5]$ . Give your answer to 3 decimal places.

[4]

3.7.2 Numerical methods (A-level only)

Question 16

3.7.2 Numerical methods (A-level only) Questions

3.7.2 Numerical methods (A-level only)

Question 16

3.7.2 Numerical methods (A-level only) Questions