Show that the process X(t) = A cos At + B sin At (where A and B are RVs) is wide-sense stationary, if (i) E(A) = E(B) = 0, (ii) E(A?) = E(B?) and (iii) E(AB) = 0 %3D

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

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Q: Part 1: A. Differentiate the following functions with respect to x y = xe ²x (ii) y = 2x³ cos x…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: What is the phase shift for the function f (x) = cos (x +)? State the direction.

A: NOTE: Refresh your page if you can't see any equations. . factor out 1/3

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: 4. Find f. (a) f'(x) = 1+3Va, f(4) = 25 (b) f"(0) = sin(0) +cos(0), f(0) = 3, f'(0) =

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Q: If f(z) = 2 sin I +3 cos z, then f'(x) = %3D

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Q: T (8) If g(x) = sin(x) *cos(x) find g'(-).

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Q: Find f. a) f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 8   b) A particle is moving…

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Q: Find f. f"(0) = sin(0) + cos(60), f(0) = 3, f'(0) = 1 f(0) = %3D

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Q: If f"(x) = V - cos(x). f'(0) = 2, and f(0) = 0, find f(x). %3D

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Q: Given that f"(x) = cos(x), f'(T/2) = 8 and f(T/2) = 7, find: %3D f'(z) =O %3D f(2) =U

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Q: Given that f"(x) = cos(x), f'(T/2) = 2 and f(T/2) = 12 find: %3D - f'(x) = f(x) =

A: Given: f''(x)=cosx

Q: Let h(x) = tan(2x + 3). Then h' (2) is and h'' (2) is

A: given function    h(x)=tan(2x+3)

Q: Consider the following function. f"(0) = sin(0) + cos(0) Find f' if f'(0) = 4. f'(0) = %3D Find f if…

A: Given the functionf"(θ)=sinθ+cosθ          .......(1)

Q: Find f(x), where f'(x) = sin(x) + cos(x) + 1 and f(#)=2. %3D %3D

A: Using anti derivative formula.

Q: Given that f" (x) = cos(x), f' (t/2) = 4 and f(r/2) = 7 find: f'(x) = f(x) =

A: We integrate our function for calculating the desired value and use the given conditions.

Q: Find f. f"(0) = sin(0) + cos(0), f(0) = 1, f'(0) = 4 %3D %D

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Q: (b) Suppose you wanted to use the sample data to decide if there is evidence that the average time…

A: Given information  Claim :  Average time spent playing video or computer games for male Canadian…

Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

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Q: 5. A tank contains 100 gal of water and 50 lbs of salt. Water containing a salt concentration of (1…

A: (a)Given that a tank contains 100 gal of water, and 50 lbs of salt.The water with the salt flows in…

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: on Find an equation for the function f(x) whose derivative is f'(x) = 4sin(8x) and whose graph…

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Q: Find F(s). F(s) = L{e-⁹t cos(2t)}

A: We have to find .

Q: f(x) = 2 sin x + 8 cos x, then f'(a): f'(x) = f'(5) = |

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Q: Given that f"(x) = cos(x), f'(x/2) = 4 and f(r/2) = 7 find: f' (x) = sinx+3 f(x) =

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Q: Let f(z) = sin(z"). %3D f'(x) = 3x cos ) COS f'(4) =| 0

A: The given function is  f(x) = sin(x3)  We have to find the value of  f'(4) .

Q: Let y = g(x) cos (In x). Compute y'(1), if g(1) = 1 and g'(1) = -2.

A: We have to find the derivative of y at x=1

Q: If f(x) = csc(3x). then f' (x) = %3D o -3csc(3x)cot(3x) o -3csc2 (3x) o 3sec(3x)tan(3x) o 3tan? (3x)

A: Given: fx=csc3x To evaluate: f'(x)

Q: The table below is a record of the number of miles driven between stops for gas and the amount of…

A: The table below is a record of the number of miles driven between stops for gas and the amount of…