Answer:
- (a) -10.13569485
- (a) 4.86693212
Explanation:
You want the approximate value of f'(0.50) if f(x) = 5ln(3x) +6cos(3 -7x) and the approximate value of f'(4.645) if f(x) = ln(3x) +sin(5x -4) -3 using centered differencing and h = 0.001 and 0.002, respectively.
Centered differencing
The approximate derivative using centered differencing is computed as ...
f'(x) ≈ ((f(x +h) -f(x -h))/(2h)
F'(0.50)
The calculations using the above formula for (x, h) = (0.50, 0.001) are shown in the first half of the attachment. The approximate value is ...
f'(0.50) ≈ -10.13569485
F'(4.645)
The calculations using the above formula for (x, h) = (4.645, 0.002) are shown in the second half of the attachment. The approximate value is ...
f'(4.645) ≈ 4.86693212
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Additional comment
The calculator must be in radians mode for these functions.
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