Consider the given function and the given interval. f(x) = 6 sin(x) - 3 sin(2x), [0, n] (a) Find the average value fave of f on the given interval. fave = (b) Find c such that fave = f(c). (Round your answers to three decimal places.) X (smaller value) X (larger value)

Q: Find the derivative, f'(x), for f(x) = S dr 3 sinr+2 (₁²³+√7) X A f(x) = B f(x)= −sinx − 2 x²³+√√x X…

A:

Q: ifferentiate each function. a) y= /6x² – 12 (b) g(x) = (cos 0 sin 0)4 (c) f(x) = sin (3x)

A:

Q: f(x) = 3 sin(2x) sin-1(2x), find f'(æ). "(x) =

A:

Q: ​f(x)= -2 sin 2 x on the interval [−π​,π​] Find where increasing and decreasing on the interva

A:

Q: sin i dt 48. Let F(x) = | Show that x3 F(x) = x - x5 x7 +... 3. 3! 5. 5! 7.7! Evaluate F(1) to three…

A: Given integral is: Fx=∫0xsin ttdt Fx=x-x33·3!+x55·5!-........... We have to find F(1).

Q: e average value of the function f(x) = 4x on the interval 0 < x < 2

A: See the details solution in below

Q: The derivative of the function f(x)= 3sin²(x) is: f '(x) = 6 sin xcos x f '(x) = - 6 sinx cos x O…

A: Given that fx=3 sin2x Differentiate the given function with respect to x. ddxfx=ddx3…

Q: What is the second derivative of f (x) =csch¬'(tan(x))? A f"(x)=- sec2(x) B) None of the given…

A:

Q: If f(x) = sin(x), which of the functions or theorems describes the average rate of change of f(x)…

A: Solution

Q: ifferentiate the function: y=(x^4 sin^2(x))^(3)

A:

Q: Find the first derivative of the function f(x) = sin (x) . a) O f'(x) = 3sin?(x) b) O f(x) =…

A:

Q: f"(x) = 5ex - 8 sin(x), (0) = 3, f(x) = 5+ 5e + 5e* + 8 sin(x) – 1

A:

Q: Estimate `sin(-0.01)` using an appropriate linear approximation L(x) = f(a) + f'(a)(x – a).…

A:

Q: a) Find the first derivative of the followings: i) f(x) = sec²x tan/x ii) f(u) = cos²(sin(1 – u)-1)…

A: We have to find out the derivative

Q: 7 sin x Let f(x) 6 sin x + 2 cos x Then f'(x) = The equation of the tangent line to y = f(x) at a =…

A:

Q: Consider the given function and the given interval. f(x) = 18 sin(x) – 9 sin(2x), [0, x] (a) Find…

A: Average value fave of f(x) on the given interval [a, b] is given by -…

Q: Find the critical numbers of the function. H(x) = sin^2x + cos x 0 < x < 2pi

A: For Critical points, put first Derivative of function equal to 0

Q: Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x))? at which the tangent line…

A:

Q: Find local and extreme values of f(x) = x + sin x, [0, 1].

A:

Q: Evaluate: sin-l z = - cos™(-3+j5) O -5.074-j2.957 -5.074-j2.957 D-5.074+j2.957 5.074+j2.957

A:

Q: Evaluate the derivative a. h(x)= (sin x + 2cos x)^1/2

A: The given function is hx=sinx+2cosx12.

Q: The height of an arch above the ground is given by the function y = 10 cos x for - 5 SXS5. What is…

A: The height of an arch above the ground is given by the function y=cosx for -π2≤x≤π2. What is the…

Q: Given the function: f (z) the value of the third derivative at x=2 using %3D sin(z) four point…

A: The function is fx=x2+xcosxsinx. The formula to find the third derivative using the four-point…

Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression, the average…

A: we have been given f(x)=sinx, g(x)=cosx and h(x)=2x. we have to find the exact value of the…

Q: [cos x - sin x 0] cos x 1] 5. If f(x) = | sin x 0|, show that f (a)f(b) = f(a + b).

A: f(x)=cosx-sinx0sinxcosx0001

Q: c Functions. Prove the identity cosh x – sinh x = e x-

A: We have to show the given condition

Q: a) Find the first derivative of the followings: i) f (x) = sec²x tan/x ii) f (u) = cos²(sin(1 –…

A: We have to find the first derivative of given function

Q: 1. Plot the function f(t) = 5 sin(x) x+e-0.75x 5 3x for -5 sxs 10. Make two separate plots of the…

A: (1) given function is                                   f(x)=5sinxx+e-0.75x-3x5; -5≤x≤10

Q: Find the derivatives of the function f for  n = 1, 2, 3, and 4. f(x) = xn sin x

A: Given : f(x) = xn sin x To determine the derivative of f(x) for n = 1,2,3 and 4

Q: 4. Express the function f(x) = 11 sin x +7 cos x as a function in terms of sine. Express your answer…

A: To find 11sinx+7cosx in terms of sine function only.

Q: 11 sin () Calculate the average of f(x) = over the interval [1,2]. (Use decimal notation. Give your…

A:

Q: Write the equation of the normal line (a line perpendicular to the tangent line) to f(x)=2−cosx at…

A:

Q: Find a0 of the function f(x) = sin(x/2

A: Given function is:  fx=sinx2

Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: Find the average rate of change of the function over the given interval.

A: Given, f(x)=sin(x);  over the interval 0,π4

Q: f(x)=-7x(sin(x)+cos(x)) f’(pi/4)=?

A:

Q: Using Newton's method, the approximation of the root x* of f(x) = 2 – x² – sinx accurate to within…

A: given function is                                              f(x)=2-x2-sinxx0=-1.6 we have to find…

Q: f(x) = 10 cos x + 5 sin 2x   Determine the points in the interval (0, 2π) at which the graph of the…

A: For finding the points on a function f(x), at which, f(x) has horizontal tangent line, we need to…

Q: Scos“ x- sin' xdx x•sin³ xdx 3

A:

Q: Find local and extreme values of f(x) = x + sin r, [0, T].

A: To find the local and extreme value of f(x) = x + sin x, [0, pi] f'(x) = 1+cos x f'(x) = 0 1+cos x =…

Q: 1. A cable that weighs 2 kg/meter is used to lift 500 kg of coal up a mine shaft 200 meters deep.…

A: Total work done = lifting the weight +                                               lifting the…

Q: f(x) = e-x (3.2 sin(x) - 0.5 cos(x))

A: Here a simple python script written follow that.

Q: cos2x - sin2x cos2x / cosx - sinx) dx=1/3 F(x) + C. What is F(x)

A:

Q: Using FPI, find a critical point of the function: f(x) = x? – 2e* cos x With an initial guess, x, =…

A: Given function: fx=x2 - 2ex cos x Find the critical point of the given function Initial Guess:…

Q: Question 13 Let f (x) =x - sin(x²). what is the correct result of the derivative of f with respect…

A:

Q: 9 sin () Calculate the average of f(x) = over the interval [1, 2]. %3D (Use decimal notation. Give…

A: Calculate the average of the given function.

Q: sinx +cos, x 0 Q4) Show that the function f(x)= is continuous at x 0 2, x 0 Q5) Determine the value…

A: See the attachment

Q: Find the first derivative or f’(x) of the following functions using the techniques of integration:

A: Given,            fx=40015-x23x-2To find : The first derivative or f’(x) of the given function.

Q: 12. What is the average rate of change of f(x) = sin- on the interval 0,? Is there a value of (3) c…

A: