Question 11 /4-x² c 3-x²-y² STS xdz dy dx Evaluate the iterated integral. J. J. -5+x²+y? 0, A) 128/15 B 16/89 c) 23/6 D) 6

Q: Evaluate the iterated integral: x + 4y dx dy Answer :

A: We can solve as follows

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function is: f(x)=e-5x

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A: Vector equation of a line passing through P(a,b,c), Q(p,q,r) is given by,…

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: To find the area of the region bounded by the given curves.

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Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

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A: Given :∑n=1∞ 1n!

Q: ind lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 E the limit does not exist, enter…

A: Topic  = Limits

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A:

Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

A: To find the area of the region enclosed by the given curves.

Q: 34 Count lim (1+x) F b) lim (1-x)* メ→0 The limit in (a) determines e. What special number does the…

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Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -162 -108

A: ∫02∫-162y2∫-108zyz dx dz dy∫-108zyz dx=(xyz)-108z…

Q: 16. Find the volume of the region that lies under the graph of the paraboloid z = over the rectangle…

A: Here, to find the volume of the paraboloid z=x2+y2+2 over the rectangle R=(x,y)∈ℝ2|-1≤x≤2, 0≤y≤2

Q: Find fr(t) u(t)] and fr(t) x u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j + tk…

A: Vector

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Q: Find the unit tangent vector to the curve at the specified value of the parameten r(t) = 4 cos(t)i +…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

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A:

Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

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Q: Represent the plane curve by a vector-valued function

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

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Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Edit Evaluate the line integral -ydx + xdy along the curve C : y = 21x from (21, 21) to (0,0). NOTE:…

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Q: Find V (V x F) if F(x, y, z) = 5 sin xi + 9 cos(x – 2y)j+ zk. V. (V × F) =

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Q: ||r'(t) x r' r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||* r(t) = t'i+ t5j K(t) =

A:

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A: Let's find.

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Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

A:

Q: Evaluate I| xy dA where R is the region in y = x2 A) 13/7 B) 16/3 18 D) 20

A: We have to evaluate the integral.

Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

A:

Q: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

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Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

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Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2 A) 1/3 B) 1/4 © 1/5 D 1/6

A: To find the area enclosed between the two given curves.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x and…

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A: Trigonometry

Q: y=x*(1-x)ª 4-4x 4+4x

A: Use the chain rule of differentiation.

Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

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A: Volume of revolution

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Q: Find the area of the region enclosed by x2 and y = 5x by integrating with respect to y. the curves Y…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: What is the volume of the largest cone having its circular base circumscribed about a face of a…

A: To determine the volume of the largest cone having its circular base circumscribed about a face of a…

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = ell'i+e"j -t. K(t) = %3D

A: