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: 4 + 4sin (x)dx = O a. 3n O b. 2n O c. 2+ 2n O d. 2+37 O e. 47 O f. 2+47

A: See the details solution in below

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Q: If f(x, y) = x cosy + ye*, find a2f дхду

A: Partial derivative: A partial derivative of a function is defined as the derivative of the function…

Q: 7. Evaluate (5 – x)dA where R {(x, y) : 0 < x < 5,0 < y < 3}

A: Double integral

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Q: 8 Find the length of a diagonal of a rectangle of length 9 cm and width 4 cm 12. A square has…

A: You must have an idea of Pathagorean Theorem to solve these problems.

Q: dy Calculate dx You need not expand your answer. E+2) x- O a. Ob. 1 Vx + 4x /x + x, Oc. x + 1 4 d.…

A: Product rule of derivative is : (d/dx)(f•g) (f • g) ' = f ' • g + f • g ' Here f ' = d f / d x and…

Q: ir6 f(c)dz = 4 and , f(x)dr – 6, th then f(z)dz = Select one. O a -2 O b-10 Oc 2 Od. 10

A: We will let that the integration of the function f(x) is g(x) to solve the question.

Q: I x In y dA, R = [0, 3] × [1, e] 43.

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Q: 4. Given: y =21 –31 and x =u – 3u , find y'

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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: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

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Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: 2x sinh ( − y) + 2axy, sinh (x – y) −3Vy − z ta, 62 Vy – Let C be the line segment from (−1, 1, 1)…

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Q: 3. Let f(x, y) = x³ 3x² + xy +7 and u = 0.6i + 0.8j, then find Duf(1,-2).

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Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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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: Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w v2 fuu + u² fov – 2uv fuv - ufu - vf dx2

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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: 15. m/DBC = Given that DA = DC, m / DBC = (10y + 3)°, and m/DBA = (8y + 10)°, find m/DBC. B C

A: Topic = Geometry

Q: when u = 0, v =1 if du Use Chain Rule to find z = sin ry + x sin y, r= u² + v² and y= uv.

A: Given: z=sinxy+xsiny, x=u2+v2 and y=uv. To find: ∂z∂u at u=0, v=1. Solution: Partial derivative of a…

Q: 2 3 c) f[(x*y +1) dx dy answer: 10.5 1 2

A: ∫∫R f(x,y) dA =∫y1y2∫x1x2 f(x,y) dx dy   or  ∫x1x2∫y1y2 f(x,y) dy dx

Q: dy If y=u? and u = x3 + 4 determine dx

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Q: f(x, y, z) fxyz In (4xy) 22 Let + sin(xy² + ye²). Find

A: Note:    We use the following notation fxyz=∂∂z∂∂y∂f∂x

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: Cl + x )y' = x"y"

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Q: Find the slope of the graph of the function at the given input value. Round your answer to three…

A: Given that f(x)= 3x - 3x. And at x=6 find the slope of the graph of this function.     Here i…

Q: 1. Solve for the variable x. F = kx – kxo A. x=F-kxg А. х- O B. x=F-kx, k F- Kxo О с.х3 C. x= D.…

A: The given equation is F=kx-kx0

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

A: partial derivative

Q: 1) 4 + y² + (9 +x?) = 0 %3D

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Q: xxx, xy(Rxy →→~Ryx) - vx~Rxx

A: To prove ∃x Rxx , ∀x∀yRxy→~Ryx ⊦∀x ~Rxx

Q: If y = In(x² + y²) then the value of d at the point (1,0) is %3D Select one: O a. 0 O b. 1/2 O c.1 O…

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