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Numerical differentiation using various methods with evenly spaced points

Numerical differentiation is mainly used for?

a: Finding values of integrals Explanation

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b: Estimating rate of change from discrete data Explanation

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c: Drawing 3D models Explanation

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d: Solving algebraic equations Explanation

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The truncation error in Forward Difference method is of order:

a: O(h) Explanation

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b: O(h²) Explanation

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c: O(1) Explanation

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d: O(h³) Explanation

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Central Difference method provides higher accuracy because:

a: It uses more data points Explanation

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b: It cancels first-order error terms Explanation

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c: It reduces rounding error completely Explanation

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d: It uses integration Explanation

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If step size h becomes extremely small, the total error may increase due to:

a: Increased truncation error Explanation

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b: Increased rounding error Explanation

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c: Polynomial degree Explanation

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d: Loss of data points Explanation

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Backward Difference method is especially useful at:

a: The first point of the dataset Explanation

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b: The last point of the dataset Explanation

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c: Any interior point Explanation

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d: Points where function is continuous Explanation

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The optimal step size in numerical differentiation is determined by:

a: Only truncation error Explanation

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b: Only rounding error Explanation

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c: Balance between truncation and rounding errors Explanation

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d: Graph resolution Explanation

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Numerical differentiation amplifies noise because:

a: Differentiation increases sensitivity to small fluctuations Explanation

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b: It reduces function smoothness Explanation

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c: It removes data points Explanation

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d: It applies integration Explanation

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The second derivative using central difference has order of accuracy:

a: O(h) Explanation

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b: O(h²) Explanation

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c: O(h³) Explanation

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d: O(1) Explanation

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In practical engineering applications, numerical differentiation is commonly used to compute:

a: Velocity and acceleration from position data Explanation

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b: Matrix determinants Explanation

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c: Eigenvalues only Explanation

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d: Integral transforms Explanation

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Which method cannot be applied directly at boundary points?

a: Forward Difference Explanation

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b: Backward Difference Explanation

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c: Central Difference Explanation

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d: All methods Explanation

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