Numerical Methods Q#19

We are using the O(h) Backward Difference formula to estimate the first derivative f'(x) at x = 1.75 where f(x) = e^x using a step size h = 0.05. If we keep halving the step size h to obtain 2 significant digits in f'(x), without any extrapolations, the final step size h will be a) 0.05/2 b) 0.05/4 c) 0.05/16 d) 0.05/8

0.05/8

Given the following table of values, the second derivative f''(x) at x = 0.9 using Backward-Difference O(h2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) 1.4900 b) 2.7700 c) 4.2600 d) 1.3400

1.3400

Given the following table of values, the second derivative f''(x) at x = 0.7 using Central-Difference O(h^2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) 12.7200 b) 9.8000 c) 5.7500 d) 7.0300

12.7200

Using the O(h) Forward Difference formula with a step size h = 0.2, the first derivative of the function f(x) = 5e^(2.3x) at x = 1.25 is a) 258.8 b) 203.8 c) 163.4 d) 211.1

258.8

Given the following table of values, the second derivative f''(x) at x = 0.9 using Central-Difference O(h2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) 1.3400 b) 2.7700 c) 4.2600 d) 1.4900

4.2600

Given the following table of values, the second derivative f''(x) at x = 0.7 using Forward-Difference O(h2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) 9.8000 b) 12.7200 c) 5.7500 d) 7.0300

9.8000

Given the following table of values, the first derivative f'(x) at x = 0.9 using Backward-Difference O(h2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) -0.2315 b) -0.3700 c) -0.0185 d) -0.7960

-0.2315

Given the following table of values, the first derivative f'(x) at x = 0.9 using Central-Difference O(h2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) -0.3700 b) -0.0185 c) -0.2315 d) -0.7960

-0.3700

Given the following table of values, the first derivative f'(x) at x = 0.7 using Forward-Difference O(h^2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) -0.7960 b) -0.9345 c) -1.9920 d) -1.6375

-1.6375

Given the following table of values, the first derivative f'(x) at x = 0.7 using Central-Difference O(h^2) formula is x | 0.6 | 0.7 | 0.8 | 0.9 | f(x) | 3.1767 | 2.9209 | 2.7923 | 2.7340 | x | 1.0 | f(x) | 2.7183 | a) -1.9920 b) -1.63775 c) -0.7960 d) -0.9345

-1.9920