If Y(t) = X(t + a) – X(t – a), prove that R, R. (T- 2a). Hence prove that Sy„(@) = 4 sin“ ao S„(@) = 2 R(T) – R(T + 2a) - %3D

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

A: The given function is

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: PLS HELP ASAP ON ALL

A: 4. Given:f(x)=π2Getting the derivative, we have:f′(x)=dxd​(π2)Since π is a constant, the derivative,…

Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

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Q: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: Let 7(t) = Find '(t) F (t) =

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Q: Let f(1) = (1 + 2x + 2)*

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Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: Let f" (x) = 6x - sin x. ƒ' (0) = 1, f(0) = 2. Find f(x) ○ x³ O x³ + sin x + 2 ○ x³ – sin x + 2 ○ x³…

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Q: f(x) = Cos (3x) as a 6th degree polynomial centered at x = 0. Hint use the following: P₂(x) = ƒ(0) +…

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Q: If y = (cos (2³) + 3)4, then equals dy dt a) 4 (cos (2³) + 3) ³ (x²) b) 4 (cos(x³) + 3)³ (-sin(x³))…

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Q: Let f"(t) = 2t + sin t, f(0) = 1 and f'(0) = 2. Evaluate f(27).

A: