Find the average value of f(x) = sin³ x cos³x on the interval [0,1].

Q: Find the derivatives of the function x=a (cos t + sin t ) ,y=a(sin t -t cos t

A: To find the derivatives of the function

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: Determine the constants a and b such that                                                       sin…

A:

Q: Find f. f"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4

A: Given functionf"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4we have to find , f(θ)

Q: find the average vaim of the function fcx) = x² = 5x + 6 cosx on th Interval [-1, [-1,3].

A:

Q: 8x sec2(x) on the interval [0, T/4]. Calculate the average value of f(x)

A: According to the given information it is required to calculate the average value of the function

Q: nd the equation of the normal line at x = given g(0) = 2 cos 0 + sin² G

A: We have to find

Q: Compute the area bounded by the cardioid r(0) =1– sin(0) on 0, Express your answer as a decimal…

A:

Q: Define f = sin(px^3)+cos(qx)^2 as a function of x (with p and q constant) and differentiate with…

A: see 2nd step.

Q: What is the average value of f(x), between x = 0 and x = 5 for f(x) = 2 + sin(x)?

A: The average value of f(x) between x=a to x= b  is     dx

Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

Q: -3 Let f(x) %3D (a) Using the definition of derivative, show that the derivative is f'(x)

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Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

A:

Q: Let f(x) = x tan what would f'(x) equal?

A:

Q: Let F be the function given by F (x) = S" (sec² (5t) – 1) dt. Which of the following is an…

A: We have given that   F(x) = ∫2x(sec2(5t)-1)dt        ...(1). And we have to find F'(x). To find the…