35. A particle travels along a curve y = f(x) as in Figure 15. Let L(t) be the particle's distance from the origin. x+ f(x)f'(x)\ dx (a) Show that dL - if the particle's location at time t is P = (x, f(x)). dt Vx² + f(x)² ) dt (b) Calculate L'(t) when x = 1 and x = 2 if f(x) = 3x² – 8x +9 and dx/dt = 4. y = f(x) FIGURE 15

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A: We will find the value of F'12 where Fx=2 cos-1x in the following step.

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A:

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A:

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Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

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A:

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A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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A: