1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: 5. In AABC, m2B = 90°. sin A = 2x + 1.5 and cos C = 3x – 0.9. Find x.

A: Given: In Triangle ABC∠B=90οsinA=2x+1.5cosC=3x−0.9x=?

Q: x cos 2x e3¤ (e) - Va) [z (P) d [2

A: d/dx(uv) = vdu/dx + udv/dx  d/dx(u/v) =( vdu/dx - udv/dx )/ v^2  d/dx(u+v) = du/dx + dv/dx

Q: Use a CAS to plot the implicitly defined level surfaces in Exercises 73–76.

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Q: 3 cos (x) sin (x) dx = %3D 2 15 O None 6

A: To find the value of given ∫0π23cos2xsin3xdx

Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: ー1 B Cos (2 oin (oen 3 + cas の An

A: Sin(A+B)=sinAcosB+sinBcosA

Q: ди k > 0 at Ans. u = e'(A,eka! cosh ax + Bjekai sinh œx) u = e¯'(A2e' u = e"(Azx + B3) k ¯kai 'cos…

A: The given problem is to find the solution for the given partial differential equation in different…

Q: 10. 3 J√cos z sin ³ zdz COS

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Q: 20. Which of the following is not an antiderivative of the function f(0) = sine cose? 1 A. B. 2 sin…

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Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.…

Q: 1. If we are trying to evaluate thef esinx cos x dx, which substitution would be most helpful? А. и…

A: Select the correct option?

Q: Which of the following is a possible solution to y" +ky =0 O y = ekz O y = cosk'a O y= k sinI O y =…

A: If roots of the auxiliary equation are imaginary i.e, α±iβ then complete solution is…

Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

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Q: 8. 3. (1 – cos wt) where w is a positive constant

A: In given options, 4 is taken instead of "w^2".  The solution for the asked question with correct…

Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y =…

A: Topic :- Derivative Correct option = C

Q: A) None 3 В) 512 Зл 256 3 256 Зл 512 (C) (D) Ε) sin√xcos√x √x E -dx is equal to

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Q: 1. Find the following antiderivatives: (b) (cos(5e) - sin(21)) dt eat (c) -2t dt 2

A: As per guideline we have to solve only three

Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

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Q: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

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Q: -) sin A = d.) cos M = 34 25 hy 16 24 30 K e.) sin L = f.) tan G = M. 7. K 8. 15

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3e'x In cos2x Vxy = 1 y? x+1 7 In (xy)-3sin 2y |- 2y = 0

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Q: e csc 20 In (ecos 2 ) Ince cos CoS 20 28) Sin2 20 OP

A: Given integral is ∫ecsc2θlnecos2θsin22θdθ since lnex=x, so lnecos2θ=cos2θ The integral becomes…

Q: If sin x = siny = a and cosx = cosy = b, then cos(x-y) is Select one: O a. z2 + a² O b. 2b + 2a O C.…

A: Given  sin x = sin y = acos x = cos y = b Use cos (x-y) formula cos(x-y)=cosx cos y + sinx sinysin…

Q: If f(1, y) = e“ sin 7y, then fay is given by: o - 28 et sin 7y O - 28 e“ cos 7y O 28 e" sin 7y O 28…

A: Given that: f(x,y)=e4x.sin7y

Q: Which of the following is equivalent to u=-cost+v3 sint ? a) u = 2 cos t +- 1 b) u = – cos| t+ 2 3…

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Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: 1. r(t) = ti + (In cos t)j, -T/2 < t < T/2

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: ad boda noY BAJUM 7. Find dy/de. dimil nom y = sin [cos(tan 0)]

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Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: Let y=9 In(cos(a). in(co(e*). dy = AeBt sinC (e6t) Then dt cosº (e6t) where A = B = C = D =

A: Given expression y=9lncose6t Differentiate the above expression w.r.t "t" dydt=9ddtlncose6t Recall…

Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: 1+ cos(t) 1 – sin(t) 2t) (n) y(t): (o) y(t) = In(5tª + 3t2 + 1) (p) y(t) = t° + T' + e™

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Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

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Q: /Prove that the value of cos()dz, when z = T + 2i is e + e-1

A: Complex integration of the function

Q: Suppose sin(0) = and 0 < 0<T/2. Compute cos(0). (Hint: SOH-CAH-TOA) V3 3 3

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Q: # 2. So sin 32 dz C: Izl=3 (z-5)

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Q: 2 (cos Fe tisin) - fsih 똥) Q) put Vz (cos 3+P sin I) 6. in expoitial hor m

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Q: 10. If h(x) = x²2cos 2x, then h'(1) = A. 4cos 2 B. 2· 2cos 2x (1 + In 2) C. 21+cos 2 D. 21+cos 2 (1…

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Q: "+25y 4r sin(51) – 2e" cos(5t)

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Q: integrate cos^2(t)*sin^2(t) from 0 to 1

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Q: (be + 10a9 – 4 sin a)da 5e* – *10 + 4cos * +e 5e + a10 – 4 sin a + e 5e + a10 – 4cos +e 5e" + a10 +…

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Q: S sin³x /cosxdx =? O a. cosT cos³z + C 3 Ob. cosr +cosz ) Vcosa + C Oc. 27/2, ) +C Od. (cos*z -…

A: Given: ∫sin3xcosxdx To determine: The value of given integral.

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: Solve the following problem = 0; (x, y) E (0, 1) × (0,1), + u(0, y) = u(x, 0) = u(1,y) = 0, и(т, 1)…

A: In this question, we have to solve the Laplace equation by separation of the variable.

Q: -1 (x³+y³ ,3. then xdw dw +y dy If w = tan x-y sin(w) sin(2w) cos(2w) None of these

A: