the function f(x) = x2 − x2- 6x a. Determine the average rate of change in f(x) on each of the following intervals: −4 ≤ x ≤ −2 b. Estimate the instantaneous rate of change of the function at

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A: at x=-2, function is defined as:g(x)=-4;       if x=-2ANSWER 14:g(-2)=4

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A: answer is in next step

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A: r(t)=(2 cos(t), 2 sin(t), t)r'(t)=-2sin(t), 2cos(t), 1r'(t)=4+1 =5T(t)=r(t)r'(t)T(t)=15-2sin(t),…

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A: We can solve the given problem as follows:

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A: Slope of parallel lines are same

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Q: Jcos'xsinx dx 2.

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A: Given query is to find the value of indicated function.

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A: We have to solve question  5

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Q: *) = (" ; ') - Show that :

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Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…