Solve the separable I.V.P y' (x2 +1) = x (y² + 4), y(0) = 0. y = 2 tan(2 + In(x + 1)) y = 2 tan(In(x + 1)) C. A. B. y = tan( 2 In(x + 1)) y = 2 tan(In(x² + 1)) D.

Q: Find f. f ''(t) = 3et + 6 sin t, f(0) = 0, f(?) = 0 f(t)=

A: Solution

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

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Q: 28. Show that tan z = sin(2x) + i sinh(2y) cos(2x) + cosh (2y)

A: We can show the given identity.

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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

A:

Q: 5. (3x-17) dx / (x² - 6x + 10) 11

A: As per our guide lines we are supposed to answer only one question. Kindly repost other questions as…

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

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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) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

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: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: B) Find (dy/dx) for the following 1. y = tan2(cosx)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find dy/dx if y= cos-1 In(x+1)

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Q: post office sells 4-cent sheep stamps and 2-cent sunset stamps. Cole bought 5 stamps spent exactly…

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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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: 4. Find d²y/dx² for the following functions: a) y = sin x? cos 2x

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Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

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Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: dr (g) sin(2x) + 4 sin r

A: Sorry we can answer first question as per honor policy. Please resubmit other question as well to…

Q: f(t) = (cost, Sint, t) f'(t) = (-sint, west, 1) 1 f'(x)) = √√(-sint) ² + ((ost ) ² + 12 F(t)= -…

A: Given that Differentiate with respect to t           Therefore