1. Integrate f fe²+³dA where R = {(x, y): x² + y² ≤ 1}. Oa. (e-1) Ob. π(e-1) OC. TE c. Od. Te ле Oe. 3

Q: 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) - v sin(e) and yusin(0) + v…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: If w sinxcosy + 1, I = sint, y cost, then by chain rule when t = 7, Select one: O A. 0 О в. - соs(-…

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Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: 38. A. -arcsin x x Vx2 – a² 39. 1 В. -arccos x a2 + x2 40. 1 С. | -arccot x Va? – x2 - D. -arccs x…

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Q: Given z = g(x,y) = ln(y) . cos(2x - 3y), show 02g -(x, y) дудх 02g - (x, y) : дхду =

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Q: . Fing the coefficient of x' and x' 9 10 expanston of any x in the (22- * Find the qe from of (2+ -5…

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Q: 7. Evaluate. LL sin z da dy.

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Q: aw аnd ar aw Q1) Find if as w = x2 + 3y + z, X =r - s, y= cos (r+ s), z=e'.

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Q: | The wave functions for two waves traveling on a string are described by: y (x, t) = A sin (2mx –…

A: Given: The wave functions for two waves travelling on a string are described by: y1(x,t)=A…

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: Ay 2 sin y dz dx dy. Evaluate 0.

A: Evaluate the given integral as follows. ∫0π2∫04y∫04y2 siny dz dx dy=∫0π2∫04y2 sin y dx dy∫04y…

Q: If interest in a bank account is compounded continuously, the amount grows at a rate that is…

A: Solution: Given data, Initial amount P = $1000 rate r= 5% = 0.05 According to continuously…

Q: w csc'udu - cotu dw = 0, w(T/6) = TT CSC A. -V(3) t = w cotu B. - V(2 ) n = w cotu C. V(3) TI =w…

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Q: 2 Inx+Vx² -1)dx = .2 Select one: a. None of them b. 2ln(2 +V3)-V3 – In(2) C. 2In(2 + V3)-V3 O d.…

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Q: complote the following using ono of the "motheds of substitution". −y dx + (x + Vxy) dy = 0

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Q: (1 + ху) dx — (1 + х?) dy %3D 0.

A: (1+xy)dx-(1+x2)dy=0(1+xy)dx=(1+x2)dydydx=(1+xy)(1+x2)put y=vxdifferentiate w.r.t.…

Q: 4. Solve the ODE using Separation of Variables. X. dy - y = 2x²y dx

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Q: 77 fox) =?& gam - & gox) then find theo %3D %3D X-3 Jolut ión of thin ineg/ualit, (fog)ca) < 2.

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Q: dy .? If sin(x + y) = xy, what is the expression for dx cos(r + y) – y 1- x cos(x + y) – y B) x – 1…

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Q: find Òw and dw for the Solloing functions w= Ln (xッ2xy).cs答かうメ)

A: Given the function w=lnx2+2xy·cscx33+yx2 We have to find ∂w∂x=the partial derivative of w with…

Q: @ / Find if dy O J= \ntanh (+2 の= Cos (Cosスー) O3=109,(e CSCX +Sinx)

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

Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

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Q: Solve the IVP. Find and verify the condition num- ber. y' = -ty; 0<t < 5, y(0) = 2, 2.5.

A: The IVP is given by y'=-ty, y(0)=2. We need to solve the IVP where  0≤t≤5. The given problem can be…

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: Activity 3: Find and simply the result, if possible. 1 a. y = vx - b. y = x? + n + x" C. y = x² secx…

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: 3. y (2x+ ylny)y' ; y(1) = 1 A. can'tbe solved using the five types of ODE discussed B. y = e?y-1-…

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