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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