s+2 6) f(1)=e" cos(t) Ans. F(s)= (s+2)° +1 A(s+a)+ Bß 7) f(1)=e""(Acos(ßt)+ B sin(Bt)) Ans. F(s)= (s+a)² + ß² 8) f(t) =(t–7)u_(1) Ans. F(s)=

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

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Q: Directions: The keys to the Egyptian and Roman systems are given on this quiz. (1) 1. 6 6666 ||||…

A:

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: O t-sin(t)

A: the answer is t-sin(t)  provided the solution below with steps in step2

Q: If x²y" + xy' + (x² – ÷)y=o x >0 ,V,=x 2 sinx , and y =y;v. Which of the following equations…

A:

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: Find y' where y where y = 10 sin-1 (cos (21 z)) - tan C BARANG (18 r)

A: Given: Now,             y'=10arcsincos21x-arctan18x'     =10arcsincos21x' -arctan18x'…

Q: sinx

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Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

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Q: sec(2) tan(2) – 1 dz 3.

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Q: Evaluate sin (ax) (ax) V3 (2ах) da Cos

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Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: A particular solution of y" + y =sinx + xcosx a. x?sinx - 2xcosx) 4 b. (x?sinx – xcosx) 4 c. (x?sinx…

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Q: Differentiate y with respect to a y cos²(a) + y sin²(a) = (cos(a)+37)² Select one: O a. y' =…

A: ycos2a+ysin2a=cosa+372

Q: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: Ssin8 (3z) cos5 (3z) dz

A:

Q: f'(3i) = -i, g(7+ 2i) = 3i, g'(7 +2i) = -4. Find (f o g)'(7+2i). 4i -4i 2.

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Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: Ir x²y" + xy' + (x? - +>v =0 x >0 || | 1 - 2 sinx ,V1=X the following equations satisfied by v and y…

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Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral:

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: If x*y" + xy' + (x? - y= 0 x >0 ,V1=x 2 sinx 3D0 and y =y,v. Which of the following equations…

A:

Q: Let F = (cos(5t), sin(3t) , 5t“) and G = (t cos(5t), cos(5t), Find F +G = (5t^4)+sin(3t)+t^4(C

A: