Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).
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Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.
A: Solution
Q: cos(2) is equal 1 اخترأحد الخيارات 2-2 sin(z) dy dx dz 2 – z 4-2 r/2 sin(2z) dy dx dz 4 - z z-2 cx/2…
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Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…
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Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…
A: Given problem:-
Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]
A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]
Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…
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Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…
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Q: pin z +y 12 + cos 2 2r F(1,y, 2) =- TY + 2,- + Cos 2
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Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx
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Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…
A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…
Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).
A: Prove the given equation
Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3…
A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…
Q: 1. fcosax tan(sin ax)dx - In |cos(sin ax)|+ c ans : or In |sec(sin ax)| + c 2. Ssin(cos.x)·sin x dx…
A: Here we use the other formulas with the given one and also use substitution.
Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=
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Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D
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Q: Sešx cos 8x dx 3x [8 sin 8x - 3 cos 8x] + C A) 73 B) 73 [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x +…
A: MULTIPLE QUESTIONS: “Since you have asked multiple questions, we will solve the first question for…
Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…
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Q: If f(x,y,z)=In(x²y+sin² 12
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Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…
A: using substitution method to solve integration
Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…
A: We have to find partial derivative of z with respect to x.Given a function of two variables, ƒ ( x,…
Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…
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Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…
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Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…
A: y= sin(6x-4)
Q: What is if z = x²y+sin(ry²)? %3D dz = 2xy + y? sin(xy') az = x² + 2ay cos(xy) 8z = 2xy + y cos(xy?).…
A: The given function is z=x2y+sinxy2
Q: 2. If y = e-* cos 2x, then f'(x) = %3D
A: Given : fx = e-xcos2x
Q: dy Find if y = 5x² sin4x dr' O None -20x? cos4x – 10xsin4x 20x? cos4x + 10xsin4x O 10x? cos4x +…
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Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…
A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx
Q: + 9y = 9 sin 3x (Let y p = Ax sin 3x + Bx cos 3x.) y = C1 sin 3x + C 2 cos 3x - x sin 3x + cos 3x y…
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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: If y= x2 sin 2x, then y = А) 2х cos 2x B 2x (sin 2x - x cos 2x) C 2x (sin 2x + x cos 2x) (D) 4x cos…
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Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…
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Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=
A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…
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: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…
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Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…
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Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…
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Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…
A: x=sin (3x+2y)
Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx
A: Recall the property of definite integral:
Q: if z=ex( x cos y-y sin y ), show that ∂2z/∂x2+∂2z/∂y2=0.
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Q: 8. 4 6° sin°3ycos *3y dy
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Q: # 2. So sin 32 dz C: Izl=3 (z-5)
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Q: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…
A: We can solve this problem using initial value problem.
Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D
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Q: dy Find , if Y = (1+ cosx)sinx dæ cos3x + cos³x – sin²x O cosx + cosx – sin³x cos2x + cos²x – sin?x…
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Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de
A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx
Q: 4 2 cos y + sen²y cos² y - senty 3 cos² y 1
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Q: 2. If y = 3 sin(2x + 3) show that y" + 4y = 0
A: Given function is: y=3sin(2x+3) To show y''+4y=0 Finding first derivative of given function:…
Q: | 10(2 sin(x)) cos(x)dx if J Ax)dx = 13
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- Can you express cos(7x) in terms of powers of cos(7x) Start from: cos(7x) = cos(7x) + i * sin(7x)Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3. y = cos (1/2x + π/6) - 1 4. y = sin (3/2x + 3π/2) + 5 5. y = cos (1/2x + 1/3)After seeing the additional solution for Fx(x,y), shouldn't it be -2sin(e2x) instead of positive 2sin(e2x) since it is Fx = 0 - sin(e2x)(2)
- show that cos 6x = cos 2x (4cos2 2x-3)Prove that: Cos^4 x=1/4+(cos2x/2)+ (cos^2 2x/4) its cos squared 2x divided by 4, but i didnt want it to read like cos to the power of 22 x divided by 4.Solve exactly over the interval 0 ≤ θ ≤ 2π 1. √3 Cosθ- 2sinθ cosθ = 0 2. Cos(θ/2) - cosθ = 0 3. (C) Cos²X + 2sinX + 2 = 0