dx 3. Evaluate: S V(x+2)(3-x) A. sin-1 (*) + 3x- C.V6 +x – x² -In |x-+v6 + x – x² |+C B. sin-1 (*)- + C D. sin h-1 +C 5

Q: |(4e + 5z* – 3 sin z)dx- O 4e² – x³ +3 cos x + c O 4e? +x³ +3 cos x + c O 4e² +x³ - 3 sin a + c O…

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Q: 5- for y = (x² + 1)5 dx a)10(x² + 1)5 b) 10x(x² + 1)* c) (x² + 1)* 6- Sin 2x is equal to: a) sin x…

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Q: 0 ex) メzx-3 معارره اماسرجعادكالعودعل الماسن عنz=لا x2. xy- yーx find %3D 3 t Fcx)こx+5X+2 Find f cl Q…

A: (1) f(x)=x3-2x2-3 Find f(x) at x=2 and f'(x) at x=2 (2) x2-xy2=y3-x3 find dydx (3) f(x)=x2+5x+23…

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: Let y = eex + sin(2x), then Y + y' is equal to 2x A 4e2x + 2 sin(2x) (B None of the given choices ©…

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Q: I. Evaluate the following function below. 3 2 1. S sin'y ( 2 – 3 cos y )´dy 9 3. S sin'x dx 9 4. J…

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Q: Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) +…

A: Given,f(x,y)=e4x-sin(x+y2)-xyDifferntiating both the sides w.r.t. x…

Q: To evaluate 3cos x=1 dr. the integrand can be transformed to 1-sin2x A.) S(3cos³x + csc?x)dx B.) 3…

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Q: #2. | Ax)dzx, f(x)= (sin z, 0srs a/2 |cosr, n/2< rSA f(x)dxr. f(x): #3.

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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: Q1) Lind dy/dx of O xe 1o X +3y = 0 2 2sinx cosy=1 9 x = sec!

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: (4e + 10z-3 sin r)dr =. O 4ez + x10-3 cos T + c O 4e + x +3 sin a + c O 4e* + x10-3 sin r + c | O…

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Q: 15. Evaluate f e sin2x cos 2x dx A. 2ecos 2x + C C. 2e sin 2x В. + C 2ecos 2x D. 2esin 2x + C

A: You need to have the idea how to use substitution in integration.

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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Q: 3) = + sin (4) r = y(In y- In r+1)

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Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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Q: (4e" + 5x* + 5 cos x)dx 4e" + x + 5 cos x + c O et – x + cos x + c - O et + x5 – 5 sin x + c 4e" +…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

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Q: POS jma- 3 d 1 sin t dt %3| dx 1 1 (A) – x sin(x²) (B) sin(x²) (C) x sin(x²) (D) –sin(x²) ов O O O O

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Q: 9-x 4. Evaluate ſ, S sin(x² + y²) dy dx

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Q: 9. Determine the following antiderivatives: sec?(x) -dx- tan(x) 6. 4x (2x² + 3)°dx а. b. - sin(2x)…

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Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

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Q: (1) y = In(x+ 4)- x tan (2) xy + xy x + 3y (3) Iny e' sin

A: In this question we will use basic of calculus i.e concept of differentiation. We will simply…

Q: (4e" + 8x7 – 7 sin r)dx: O 4e" – x8 +7 cos x + c O 4e" + x8+7 cos x + c O 4e* + x* – 7 cos x + c O…

A: Explanation of the answer is as follows

Q: * (s in-(x))² dx = V1-x2 Select one: а. sin-(x) + C 1 - x? b. (sin-(x))³ + C 3 C. sin-V1 - x²) +C O…

A: With the help of substitution method, integration is solved.

Q: 32. Il sin(x + y) = x,'then dx A 1- cos(x+y) (cos(x +,pv) IB 1+ :aas(x + y) cos(x + v) C cos(x + y)…

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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: Evaluate: /sin(Vx)dx A 2/x sin(Vx) +2cos(/x)+ C B 2sin(Vx)+2/xcos(x)+ C None of the given Choices O…

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: S+ V D 1) cos (x +V x )dx = OA. 5 2. sin(x + Vx) + C Ов. 5 sin(x + 2 VxF) + C Ос. 2 sin(x + Vx) + C…

A: We have to determine the integral of the given function.

Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 3. For xe 0,1. express sin 7x = a+bx + cx² +ex³ Find values of a, b, c and e by ensuring that the…

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Q: Evaluate L{e* (cos at – sin nt s+3 A. (s+3)° – n² (s+3)² - – n² 2 S - 3 (s – 3)° – n² (s-3)° -R 2 2…

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Q: |xV4 - x dx x(x – 1)10 dx 43. 44. /* + 1°d – »° dx (x + 5)(x – 5)'/3 dx (x + 1)²(1 45. 46. |3x*VF +…

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Q: f(x) = |x|, −π<x< T 1-(-1)" a. f(x) = 2 Σ=1 sin nx n (-1)"+1 00 b. f(x) = 1 + ² =1 - 2 πT n² (-1)"-1…

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: Use graphs to evaluate 2π S 2r S 0 sin x dx = cos x dx = 2t S 0 2π sin x dx and cos x dx. 0

A: We will find the required.

Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: 3. Find the general solution of (2y cos x + sin*x)dx = sin x dy a. y = sin²x(- cos x + C) c. y =…

A: follow next step

Q: Following S sin(A) cos(B) dx = ; f sin(A + B) + sin(A – B), | what is the integral of f sin 5x cos…

A: We have to solve the following

Q: 1. L(e** + e¬* + x²) S-4 s+1 s3 e3 2. L(sin 2x + e²x+3) : 2 + s2+4 s-2 Hint: e2x+3 = (e2x)(e³) %3D…

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Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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Q: x1'=2x1 + 2x2 + t x2'=-x1 + 2x2 + sint  x1(0)=1 ve x2(0)=1 sistemini çözünüz

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Q: dx dt (b) 3x – 6x = sin 2t given that x = 1 when t = 0 (c) i- 7* + 12x = 2 given that at t = 0, x 1…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: 9. If f is an always positive, differentiable function and y = In (f (sin x)), what is- dy when x =…

A: Explanation of the answer is as follows

Q: fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13…

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Q: 11) e3x = sin(x + 8y) %3D dy A) - dx 3ex 8sin(x + 8y) 24ex dy B) dx sin(x + 8y) dy sin(x + 8y) -3ex…

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Q: Evaluate L{e" (coshrt + sin nt)} . s+3 А. (s+3) –n² (s+3) – n² S-3 В. (s–3)° -n² (s-3) – n² S | s+3…

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Q: 7. S 7.c003 4x dx A) sin 4x - sin3 4x •c B) sin 4x - cos3 4x +c 97 sin áx - sin3 4x + c D sin dx +…

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