Applications of Derivatives · Applied Problems
Differentials
The differential dy approximates the change in y for a small change dx. Used for error estimation and approximation.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
Use differentials to approximate the change in y = x³ when x changes from 2 to 2.01.
- dy = f'(x) dx = 3x² dx
- dy = 3(4)(0.01) = 0.12
Answer: dy = 0.12 (actual Δy = 0.120601)
1 more worked examplePremium
A square is measured as 10 cm on a side with a possible error of ±0.05 cm. Use differentials to estimate the error in the computed area.
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