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Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: 2cos'z = COS T Select all correct solutions.

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Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

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Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

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Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

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Q: 21. xe2x cos x dx (Hint: Let u = x*) %3D

A: The integration by parts method to integrate the product of two terms u and dv is given by the…

Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: 3. Why is u = cos x, dv = x dx a poor choice for evaluating | x cos x dx?

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: The substitution u = tan |converts the integral 2 π/3 1 dx to: n/2 2 +sin x - coS X

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: (d) lim In(cos r) エ→0

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Q: 1 Find 는 dx by using chain rule, if f = u + u = T x , at x = = 4 cos?u

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Q: C) Find a z and of xy" ay (xy2) - -군3 COs %3D

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Q: 2. If y = e-* cos 2x, then f'(x) = %3D

A: Given : fx = e-xcos2x

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: i. Jsin xcos 2x - sin 2x cos xdx

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Q: "/2 dx dy = * 4 3 cos X I then k is equal to 6. %3D %3D k

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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: .2. COS X sın.x.ços.Xdx

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Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og ys x*

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Q: /2 | cos(r)e sin z dx O a. el O b. e sin 1 C. 1—е 1 O d. cos 1

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Q: 3. Given that z = e" cos (), u = 4e2" – sin 2y, v = e" + n tan r. COS - Use chain rule to find dz/ðx…

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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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

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Q: If z=x+iy=r(cos(0) + isin(e))then

A: The given equation is z=x+iy=rcosθ+isinθ.

Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: 3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

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Q: y = In(cos“ x ) %3D

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Q: -2x 2) (² f(x, y) = e¯ fxx + fyy = 0 Consider -2y cos 2y - e cos 2x. Verify that

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Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: -2 sin x where y () = 7 dx O y = 2 cos x + C O y = -2 cos x + C

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Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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