BTEC NC - Maths - Calculus

Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

Task 11.1 Differentiate the following algebraic functions:a) y = 3 x ˉ

b)

1.2 Differentiate the following exponential functions:a)

Using the following law:

Therefore:

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

b)

1.3 Differentiate the following trigonometric functions:a)

Using the following law:

Therefore:

b)

Using the following law:

Therefore:

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

1.4 Integrate the following algebraic functions:a)

b)

1.5 Integrate the following exponential functions:a)

b)

1.6 Integrate the following trigonometric functions:a)

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

)(1

)( axCosa

axSin

b)

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

Task 2

2.1a)

b)Using the following law:

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

2.2a)

b)Using the following law:

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

Task 33.1 Mean Value of v = 10 sin θ

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Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

As you can see on the printscreen above, the area below the curve is the same as the area below the mean value line given in the equation that has been worked through, also above.

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Sin2 = ½ (1 – Cos 2x)From Standard Trigonometry Formula Sheet

Brendan Burr BTEC National Certificate in ElectronicsCalculus Methods

3.2 RMS value of v=25 sin 50 л t

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