Find the average value of the function f(x) = 2sin®(x)cos³(x) on the interval

Q: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

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: 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: 3) Find the average rate of change of the function over the given interval or intervals: f(x) = x' +…

A: The average rate of change is similar to that of a slope between two points . The average rate of…

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: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

A:

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: Differentiate the following function: 1 f(t) = Vi – f'(t) =

A:

Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

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: Differentiate the function: f(x) = x secx Select one: a. f'(x) = 3x2 • secx + x · sec x • tan x…

A: To differentiate the given function.

Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: f (x.y) =xy(3-x-3) f local extrena value=?

A: The given question is f(x,y) = x y ( 3- x - y) We can expand f to

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…