Use a double integral to find the volume under the plane z = 32x + y and over the rectangle R = {(x, y): 3 < x < 5,1 < y < 2 i cubic units

Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

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Q: (a) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) =…

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Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ei + Sin(/2)j + e stk…

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Q: Find V x (V × F) if F(x, y, z) = 6xyj+7xyzk. V × (V × F)

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Directional derivative: D f = del f • unit vector of direction

Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: (2) Prove that for any integer L () NTX / sin? dx = L. L -L

A: ∫ cos(ax) dx = 1a sin(ax) +C

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

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Q: Pu 6 • (2, 5) (4, –3) Graph of f 3. The graph of ƒ is shown above for 0 < x < 4, What is (A) –1 (B)…

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Q: Find the Laplace Transform of the following functions: a. L(sinxcosxe*} b. L{

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Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 15x from (15, 15) to (0, 0). NOTE:…

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Q: Consider the piecewise-defined function Jr+3, |1- x, x 0. (a) FUNCTION, so it must pass the…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Use the Egyptian's formula to calculate the area of a circle with diameter of 8 units. (roundoff…

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Q: Given the force field F, find the work required to move an object on the given orientated curve. F =…

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Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

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Q: -6w + x + 3y + 6z = -6 -7w - x – 9y – 2z = -33 -4w – 9x + 8y + 9z = -94 -w – 6x – 10y + 9z = -202…

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Q: Find the particular solution that satisfies the initial conditic (e* + eX), f(0) = 1, f'(0) = 0 2…

A: Here we have to find the particular solution of given differential equation.

Q: Let y = (3x + 2 sin(x))*. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A: Here the given function is: y=(3x+2sin(x))4

Q: 1- sine Evaluate the iterated integrals J. J. r2 cose dr de̟ A ) 1 В 2 (c) o D 3

A: The integration of the double integral is r2Cos(theta).

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

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Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

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Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

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Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

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Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

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: 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: 8. 1) Use the Integral Test to determine whether the series is convergent or dive n' +1 n=1 Please…

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Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 6x from (6,6) to (0,0). NOTE: Enter…

A: We need to evaluate the following line integral ∫C-ydx+xdy Where,  C: y2 = 6x  from 6, 6 to 0, 0

Q: The answer above is NOT correct. Use calculus to find the volume of a cap of a sphere with height h…

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Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

Q: Use the gradient to find the directional derivetive of the function at Pin the drecton of v n(x, y)…

A: Directional derivative of a function f(x,y) at a point P(a,b) in the direction of the vector v=ai+bj…

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

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Q: e2x - e 2x 3. lim, 0 sinx

A: To evaluate the given limit.limx→0 e2x-e-2xsin x

Q: al)= gi+ sk vio)= 5), ro) 0

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Q: Evaluate the line integral / -ydx + xdy along the curve C C : y? = 27x from (27, 27) to (0,0). NOTE:…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y³, P(4,…

A: Given :f=x3-y3

Q: I need help with this question (Not honor class) (Not grading)

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: (4x - lim (4x – V16x2 + 3x – 5

A: Topic:- limit calculation

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&amp; M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: Find V x (V x F) if F(x, y, z) = 4.xyj+ xyz k. V x (V × F) =

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Q: Find the unit tangent vector to the curve at t r(t) = t°i + 3t?j, t= 2 T(2) =

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Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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Q: Calculus solve by integration by parts

A: Our Aim is to evaluate the integral by integration by partsI=∫xx+13/2 dx  -(i)

Q: The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire…

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