Question 14 Find the area of the surface that is generated by revolving the portion of the curve y= x between x = 1 and x = 2 about the y- axis. А) 30.85 В) 1 45 D 55

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

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Q: Find the following for the given equation. r(t) = (e, 5t?, 6 tan(t)) (a) r'(t) = (b) r"(t) = (c)…

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Q: O An ellipse in the plane x axis, minor axis of length 14 parallel to the y-axis. = 1, center at (1,…

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Q: Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

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Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: cos (0 + 11) y = Use symbolic notation and fractions where needed.) dy -4 cos (0+11) sin(0+11)| do

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Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Find V x (V × F) if F(x, y, z) = 4xyj+ 9xyz k. V x (V × F)

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

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Q: the first quadrant bounded by the graphs of y = V16 – x², y = 0, andx = 0 is revolved about (a) the…

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Q: Find curl (4z i + 5x j + 3y k). Exact number, no tolerance. curl (4z i + 5x j+ 3y k) = (i )i + ( )j…

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Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

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Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

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Q: a 0 0 0 0b0 0 0 0 c 0 0 0 0 d Using cofactor method, prove that det M = = abcd

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: find in Verse, then domain t range 8-X\ = (x)} OD:[8,8),R:[O,00) 2 All Real Numbers 8.00

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Q: Fidn the sum: 2k (Write your final answer in fraction form, when applicable) A=31

A: Use the formula of summation then put the limits .

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: Question 10 Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B)…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-2 and y=x about…

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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: The graphs of the function f (r) = 7- a and g(a) = 3 are given below. %3D 10 8 f(x) = 7-x2 4- g(x) =…

A: topic- area bounded by curves

Q: 2а-2х V4a-V4x

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Q: Find f. (a) f'(x) = 3x4 – 5x? + x

A: Given query is to find the function.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: y=2\4-x²

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: [r(t)xu(t)] , in two dilferent ways Find CHE).t)] and rt)- costi + sintj +tk, u(t)=j+Ek dt (i) Find…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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

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Q: Find the volume of the solid generated by revolving about the y- axis the region bounded by the…

A: Given problem:- Find the volume of the solid generated by revolving about the y- axis the region…

Q: The graphs of the function f (r) = 7 - a and g(a) = 3 are given below. %3D

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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: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

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

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: 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: Find div F and curl F if F(x,y, z) = 4y®z³i – 7x°z*j – 3xy°k. div F=|0 curl F=

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

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Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 5 sin(t)j…

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Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: 1+9n² b) Determine whether the sequence a, = converges or diverges. If it converges, %3D 1+n find…

A: The given sequence is: an=1+9n21+n2

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = Xx. A 1 в) 4 0.5 D 3

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Q: Solve [D* +3D² –4]y= 2sin° (5x)

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Q: 8. The ideal gas law PV volume, and temperature of a confined gas, where n is the number of moles of…

A: We need to prove the statement.

Q: Find curl(3z i+ 4x j+ 8y k). curl(3z i+ 4x j + 8y k) = ( )i + ( i )j+ ( )k

A: We need to find curl of given vector.

Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

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