2. Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a. when z = (w^2 + 1)^7 (3? − 7)^4 b. when cos(w − z) = z sin w

Q: If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at…

A: At P1, 2, 3, A→=25ax+195ay+25az. As r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx, at the given point we…

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

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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…

A: The solution is given as

Q: Solve (by separation of variables) the following problem du = 0 ; x E R , t> 0, t > 0, - и(х,0) =…

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Q: 2 6 Use Fubini's Theorem to evaluate 2x exy dx dy. 00 26 2x e Xy dx dy = | (Type an exact answer.)…

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Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

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Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: Suppose that x2y" + axy' + by = 0 has the general solution of the following form: y = x-(C, cos (3…

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Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

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Q: Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw b.…

A: Given that when cos(w − z) = z sin w

Q: 3. Eliminate the Arbitrary Constants (C, and C2) in the equation. (25 pts) y = C,cos (At) – C2 sin…

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Q: Obtain the general solution of the following: 2. -z (2- 2) sec'e 3. xdx + sin () Lydx - xdy]

A: 2. The given equation is  dθdz=z(z-z2)sec2θ This can be written as…

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

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: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

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Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

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

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

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: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

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Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: Match the following guess solutions yp for the method of undetermined coefficients with the…

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Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

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Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

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: x = Cịcos (At) + C2 sin (At)

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Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

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

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Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

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Q: What happens if you can write a function as a composite in differentways? Do you get the same…

A: 39. Part a). It is given that, y=cos u and u=6x+2 Therefore, dydu=-sin u  and  dudx=6 So,…

Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

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Q: If z = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O…

A: Since you have posted multiple problems we will answer first problem for you for remaining problem…

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: If P = 2 sin(10t + x − π/4)ay and Qs = ejx (ax − az)sin πy, determine the phasor form of P and the…

A: Given- If P = 2sin10t + x - π4ay and Qs = ejxax - azsinπy To find- Determine the phasor form of P…

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: Show that y(x) = cos-(Acot x) + B is the general solution to the Euler-Lagrange equation for the…

A: Given function is, ∫1+y'sinx2dx Let, us assume that the function is, Ly',x,y=1+y'sinx2 So, the Euler…

Q: 1. Eliminate the parameter tgiven x = t – 3 sint and y = 2 + 3 cos t.

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Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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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: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: 8. Which of the following is the solution of * [2x + ycos(xy)]dx + xcos(xy)dy = 0 x? + cos(xy) =c x?…

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Q: 7. Determine the following general antiderivatives. | cos*(x) b. sin(x) xp- 10 10 | sin(x)cos(x)] d.…

A: Please see the below picture for detailed solution.

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.