Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

Task 11.1 Differentiate the following with respect to x using the Chain Rule

(Function of a Function):

Let So

The Chain Rule =

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

Replace “u” for the initial substitution.

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

1.2 Differentiate the following function with respect to x using theQuotient Rule:

By making a substitution before differentiating I can differentiate the two separate sections of the equation, as follows:

Quotient Rule:

Substitute the above values into the Quotient Rule Equation:

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

1.3 Differentiate the following function with respect to x using the Product Rule:

By making a substitution before differentiating I can differentiate the two separate sections of the equation, as follows:

Product Rule:

Substitute the above values into the Product Rule Equation:

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

1.4 The brakes are applied to a train and the velocity v at any time t secs after applying the brakes is given by:

m/s

Calculate the distance travelled in 10 seconds after the brakes are applied.

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

1.5 A sinusoidal voltage waveform is given by:

Volts

Determine the mean value of the voltage over a half cycle using definite integration.

Limits:

in Radians

Volts

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

1.6 Evaluate the following definite integral to 1 decimal place:

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

1.7 Find the area under the curve between and for the function:

Limits:

AREA:

(to 2 decimal places)

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

Task 22.1 Find by numerical integration using the trapezoidal rule the area under

the curve using 8 intervals and 2 decimal places:

Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9X 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

X Y=e^-x0.00 10.25 0.780.50 0.610.75 0.471.00 0.371.25 0.291.50 0.221.75 0.172.00 0.14

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Brendan Burr BTEC National Certificate in ElectronicsApplied Calculus

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