7. Which of the following sets of functions is linearly dependent on R[0,2″]? (a) {6, x, sin x} (b) {1, sinx, sin 2x} (c) {cos 2x, sin² x, cos²x} (d) {x, cos x}

Q: 12 3. (sin x)y' +y cos r = r sin a,

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Q: 1+sin 2 x 1) Find the derivative of f(x): 2 cos3 x

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Find f. f(0) = = f"(0) = sin(0) + cos(8), f(0) = 3, f'(0) = 2

A: f"θ=sinθ+cosθ Integrating both sides  ∫f" θdθ=∫sinθdθ+∫cosθdθ f'θ=-cosθ+sinθ+C..... (i)  Put θ=0…

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

A:

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

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

A: Objective is to find f.

Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

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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: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

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

A: Given that the expression

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: sin.x 14. What is y" if y=1-cosx A) y'= B) y'= -COS.X (1 – cosx)? sinx (1-cos.x)² C) y'= D) y'=…

A: Given: y=sinx1-cosx We have to find y''.

Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

A:

Q: L (sin? t) What is f (t), f' (t) and f (0) ? O b) O a) f (t) = sin t, f' (t) = 2 cost, f (0) = 0 f…

A: We will find out the required solution.

Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

Q: Find f. f(0) = f"(0) = sin(0) + cos(8), cos(8), f(0) = 1, f '(0) = 3

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Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

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Q: 4. Let f(x)= 5Vx and g(x)= 4 + sin x. (a) Find (f ° (x) and (f ° g'(x). (b) Find (g ºf)(x) and…

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Q: If f(z) : f'(z) =D %3D coS I - 6 tan z, then %3D

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 2/x?y" – 2xy' + 2y = x³ cos x

A:

Q: Find f. f"(8) = sin(e) + cos(e), f(0) = 5, f'(0) = 4 f(e) = 5t – sin (t) – cos(t) + 6

A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

Q: Find f. f"(e) = sin(e) + cos(e), f(0) = 5, f(0) = 4

A: f''(θ)=sin(θ)+cos(θ)Integrate with respect to θf'(θ)=∫sin(θ)+cos(θ) dθ f'(θ) =-cos(θ)+sin(θ)+C1Again…