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Approximate the value of f'(5.245) if f(x) = In(3x) + sin(5x- 4)-3 Using Forward Differencing. h = 0.025 -4.58872425 -4.534479401 O-4.73245564 5 pts -4.660589945 Question 10 Approximate the value of f"(2.156) if f(x) = 2tan(x) + cos(2x). h = 0.003 O-18.22610955 8.396938164 O8.424277328 O-18.51527191 5 pt

User Tadasajon
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1 Answer

5 votes

Answer:

9. (a) -4.58872425

10. (a) -18.22610955

Explanation:

You want the approximate value of f'(5.245) if f(x) = ln(3x) +sin(5x -4) -3 and the approximate value of f''(2.156) if f(x) = 2tan(x) +cos(2x) using h = 0.025 and 0.003, respectively.

9. f'(5.245)

The approximate value of f'(x) is the difference quotient ...

f'(x) ≈ (f(x+h) -f(x))/h

For x=5.245 and h=0.025, this is ...

f'(x) ≈ ((f(5.245 +0.025) -f(5.245))/0.025

The calculator screen in the first attachment shows the value of this is about ...

f'(5.245) ≈ -4.58872425

10. f''(2.156)

For the second derivative, we use ...

f'(x) ≈ ((f(x +h) -f(x))/h

f''(x) = (f'(x -h) -f'(x))/h

The calculator screen in the second attachment shows the calculations and the final value of f''(2.156) as ...

f''(2.156) ≈ -18.22610955

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Additional comment

Note that the calculator must be set to radians mode.

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Approximate the value of f'(5.245) if f(x) = In(3x) + sin(5x- 4)-3 Using Forward Differencing-example-1
Approximate the value of f'(5.245) if f(x) = In(3x) + sin(5x- 4)-3 Using Forward Differencing-example-2
User Kaan Burak Sener
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8.5k points