The value of the differential to 3dp is 0.159
Given the function y = sin(2x)/x
Differentiating the function using quotient rule will be;
dy/dx = [x(2cos2x) - sin(2x)]/x²
dy = [x(2cos2x) - sin(2x)]/x² dx
Given that x = pi and dx = 0.25
dy = [x(2cos2x) - sin(2x)]/x² dx
dy = [π(2cos2π) - sin(2π)]/π² (0.25)
dy = [2π-0]/π² · (0.25)
dy = 2/π · 0.25
dy = 0.5/π
dy = 0.5/3.14
dy = 0.159
Hence the value of the differential to 3dp is 0.159
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