Express the vector equation of the helix 7(1) = 2 costi + 2 sint] + tk...

    

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Express the vector equation of the helix 7(1) = 2 costi + 2 sint] + tk as a function of arc length s. Verify that 7 (s) is a unit tangent vector. - (b) Find the Fourier series for f(x) = x in the range x = 0 to x = 5. (c) Determine the half - range sine series for the function defined by f(x) = 0 < x < 1, (2-x), I < x < 2. X, [5 Marks] [6 Marks] [5 Marks] (d) Suppose that 7 (1) = 1²27 +(1²-61)) - (13 +21) is the position vector of a moving particle. At what time does the particle pass through the xz - What are its velocity and acceleration at these points? - plane? [4 Marks] Express the vector equation of the helix 7(1) = 2 costi + 2 sint] + tk as a function of arc length s. Verify that 7 (s) is a unit tangent vector. - (b) Find the Fourier series for f(x) = x in the range x = 0 to x = 5. (c) Determine the half - range sine series for the function defined by f(x) = 0 < x < 1, (2-x), I < x < 2. X, [5 Marks] [6 Marks] [5 Marks] (d) Suppose that 7 (1) = 1²27 +(1²-61)) - (13 +21) is the position vector of a moving particle. At what time does the particle pass through the xz - What are its velocity and acceleration at these points? - plane? [4 Marks]

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a The helix is defined parametrically as rt 2costi 2sintj tk To express this as a function of arc le... View the full answer