(a) PSD of U (t) = X (t) + Y (t) (b) Sxy (@) and Sxy(@)

Q: T² 2 / (x + 1) (2² + 1) dr. Evaluate

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Q: Find df/ dx of  f(x)=(x2-1)(x3+3x2/x2+2)

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Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

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Q: find (a) r'(1), (b) r"(1), and (c) r'(f) • r"(f).

A: The derivative of a position vector gives the rate of change of position of the body or the velocity…

Q: (5) (sec-i x) =, d

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Q: Find y as a function of a if y(1) = 3, y'(1) = -7. y = r²y" + 3xy' - 63y = 0,

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Q: AB1: Find g(2), g'(2), and g"(2).

A: Given that gx=∫-2x2ftdt Now we have to find g2, g'2 and g''2 In the interval -2,2, fx=4-x2In the…

Q: ((x/y)/z)+(x/(y/z))

A: In mathematics, precalculus is a set of course that includes algebra and trigonometry to prepare…

Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

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Q: f(x) = In(5 + 4x)

A: Given: - The function is, f(x)=ln(5+4x) To find: - The derivative of the given function.

Q: 2 y (4- y²)³ dy

A: The objective of the question is evaluate the definite integral.

Q: L=2-36X, y'co) =5, and ylo)=S x)

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Q: f(x) then: f'(x) = f'(1) -

A: We are asked to find the derivatives of the function.

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: (:' } - 8) zp - Vz(z – 2)

A: We use the difference of cube formula for numerator

Q: Find y' and y "   y =x2In(2x).

A: Given: y= x2ln2xDifferentiation Formula:ddxlnx=1xddxxn=nxn-1ddxuv=uv'+vu'

Q: + If x? = x-y then, y *+y

A: Given  x2=x+yx-y first we multiply each side by x-y x2x-y=x+yx-yx-y     by dividing  x-y from x - y…

Q: Let f (x) = x² 2 - 8 Find and simplify f'(x) and f" (x). + B where f'(x) = A = B = C = %3D Dx2 + E…

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Q: First derivative of ₂ F₁(x): d a {2 F₁ (a, b; c; x)} = dx a.b с 2F₁ (a +1, b+1; c + 1; x)

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Q: Finf the equation of the tangent line to (cos(x)ex10x)/(Sec2(5x)+1)+11 at the point (0,11)

A: Given,           The equation of the tangent line to (cos(x)ex10x)(sec2(5x)+1)+11  at the point…

Q: _____18) Find y' if y= 6+x √4-x²

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Q: Y(6) = cot(5s)- 3 tan s - csc (5s)- 3 sec' s s:y (s) |

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Q: f(x) b-a dx = 2 Prove f(x)+f(a+b-x) a

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Q: lo UcE - Uxx=0 4(x,0) = f(x) 4= (x2,0) = g(x)

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Q: If u(x) = x3, then du = 3x2.

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Q: (ii) Show that {Xt} is stationary.

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Q: Differentiate the functions. a) f(x) = 2 – 5x + b) f(x) = e* + cosx c) f(x) = d) f(x) = (5 – x²)· e*

A: Suppose f and g are differentiable function .Then note the following results : The power rule of…

Q: f(x) 9(2) where f(-3) = 7, f' (-3) = –9, 9(-3) = –2, and g'(-3) = 1. What is h' (-3)? Let h(x) Do…

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Q: /is [sec2(x) – csc²(x)]dx Evaluate:

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Q: 4 Let f(x) = 6x°va + || f'(x) =

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Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

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