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The derivative of f(x) = cos(x) can be estimated using the approximation
f '(x) = f(x + h) - f(x - h) 2h
The percentage error is calculated as
Exact value - Approximation value 
× 100 Exact value
The percentage error in the derivative of f(x) at x = π / 6 radian, choosing h = 0.1 radian, is
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- < 0.1%
- > 1% and < 5%
- > 0.1% and < 1%
- > 5%
- < 0.1%
Correct Option: C
f(x) = cos(x)
| at x = | rad = | × | = 30° | |||
| 6 | 6 | π |
| [f '(x)]2 = -sin30° = | .......(1) | |
| 2 |
| f '(x)= | ||
| 2h |
| ∵ x = | = 30° | |
| 6 |
| h = 0.1 = | ||
| π |
| [f '(x)]2 = | ||
| 2h |
| = | = | = -0.499 | ||
| 2h | 2 × 0.1 |
| % error = | ||
| [f '(x)]1 |
= 0.166% (> 0.1% and < 1%)
