[Solved] Why does the choice of step size h affect the accuracy of numerical differentiation in MATLAB? — Ans: Too large h causes poor approximation; too small h causes round-off errors | MATLAB

MATLAB - Numerical Methods

Why does the choice of step size h affect the accuracy of numerical differentiation in MATLAB?

AToo large h causes poor approximation; too small h causes round-off errors

BStep size h does not affect accuracy

CSmaller h always improves accuracy without limit

DLarger h always improves accuracy

Step-by-Step Solution

Solution:

Step 1: Understand truncation error
Large h causes the difference quotient to poorly approximate the derivative (truncation error).
Step 2: Understand round-off error
Very small h causes subtraction of nearly equal numbers, increasing round-off errors.
Final Answer:
Too large h causes poor approximation; too small h causes round-off errors -> Option A
Quick Check:
Step size h affects accuracy due to error trade-off [OK]

Quick Trick: Balance h to minimize truncation and round-off errors [OK]

Common Mistakes:

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