An EEG amplifier's input-output relationship is given by y=100x+0.5x2. What is the static sensitivity around the input of x=5 ? Round your answer to three significant figures.

Question

An EEG amplifier's input-output relationship is given by y=100x+0.5x2. What is the static sensitivity around the input of x=5 ? Round your answer to three significant figures.

BlackTom AI · Accepted Answer

First, identify the static sensitivity of an amplifier with an input-output relation y = 100x + 0.5x^2. Static sensitivity is the small-signal slope dy/dx evaluated at the operating point.

Next, compute the derivative dy/dx = d/dx [100x + 0.5x^2] = 100 + x. This derivative gives the instantaneous change in output per unit change in input at any input level x.

Then, substitute the operating point x = 5 into the derivative: dy/dx |_{x=5} = 100 + 5 = 105.

Finally, round to three significant figures. The value 105 already has three significant figures, so the static sensitivity around x = 5 is 105 (in the same units as y per unit x).

BN5102 Quiz 1

An EEG amplifier's input-output relationship is given by y=100x+0.5x2. What is the static sensitivity around the input of x=5 ? Round your answer to three significant figures.

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