What is correct form of the particular solution associated with the differential equationy'''=8?

Q: Q6. Evaluate S¹, S₂ Sp dz dx dy.

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Q: Calculate the determinant. jk 1 -1 9 4 0 71 기 -7i-34j+3k x

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Q: Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any…

A: Given: rt= cost i + et j + t2 k

Q: x²+1 lim x-5 √2x+2-2

A: We have to evaluate the limit.

Q: Let f(x) = 2log₁(x) f'(x)= ƒ' (6) =

A: We have to solve above question

Q: Let f be a continuous function such that D -3 f(x) dx = F 3. What is the value of f(x) dx = -2 and…

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Q: Calculate the definite integral by referring to the figure with the indicated areas. d d a f(x) dx…

A: Solution

Q: Show that (u₁. U₂. u) is an orthogonal basis for R³. Then express x as a linear combination of the…

A: Answer is in next step. please give a like !!

Q: Devin invested an amount of $10,000.00 in a mutual fund. After 2 years and 6 months the accumulated…

A: The solution is given below

Q: Evaluate the definite integrals using properties of the definite integral and the fact that 5 $S² √3…

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Q: Find fxx(x,y), fxy(x,y), fyx (x,y), and fyy (x,y) for the function f. f(x,y) = 9x e 9xy fxx (x,y)=…

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Q: A lamp post 3m high is 6m from a wall. A man 2m tall is walking directly from  the post toward the…

A: Given:- The given lamp post 3m high is 6m from a wall The given man's height is 2m The man is…

Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: = Approximate the area under the curve y with 4 subdivisions. x³ from x = 2 to 4 using a Right…

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Q: Consider the function f(t) = 5 sec²(t) — 9t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: Solve the following first order differential equation: dy y² +49 +3 35 4 x² + 2x³-3x² dx == 0 given…

A: Differential equation: 35x4+2x3-3x2·dydx-y2+49x3=0

Q: Problem Set #1. (w/Answer Key) 1. x²y' = x²+1 3y² +1 1. y(y² + 1) = (x² + Cx - 1) X

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Q: Solve the differential equation xdy]=0 xdx +sin? (%) [yde 4x ln || - 2y + x sin ( ² ) = 0 2x a. 2y…

A: Given :   xdx+sin2yxydx-xdy=0

Q: Use cylindrical coordinates to integrate f(x, y, z) = z over the intersection (i.e. all the volume…

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Q: For the curve given by the vvf r(t) = ti + 2t²j+t³k, find the unit tangent T(t), principal normal…

A: I have appended the formula used in the solution part of the question

Q: Evaluate the definite integral using Part 1 of the Fundamental Theorem of Calculus. 6² Enter the…

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Q: Suppose that f(x, y) = 5, and D = {(x, y) | x² + y² ≤ 1}. Then the double integral of f(x, y) over D…

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Q: Find the Taylor Series generated by f(x) = (7 · X) ² at X=6 : f'(x) =__9 (7-X) 10 90 ƒ"(x)= (7-x)"…

A: The given function is fx=17-x9 centered at x=6

Q: Find the local extrema of the following function. f(x,y) = x³ - 3xy² +12y² For the critical points…

A: the solution is given below

Q: For the given function find an equation for the inverse function f-1(x).  f(x)=3x-1

A: To find out the inverse of the function given.

Q: Evaluate the indefinite integral. 5 fz¹ √8+zºdz + C

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Q: tan x-sec²x +3=0

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Q: Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

A: This question is related to differentiation, We will solve it using given information.

Q: (b) Sketch, on separate graphs, each of the following functions (ii) sech(x). (iii) coth(x).

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Q: Let f(x) = 10x + 12 - 9e. Then the equation of the tangent line to the graph of f(x) at the point…

A: given f(x)=10x+12-9ex

Q: ✓cos x lim x 0 1 cos x - -

A: The given limit is limx→01-cosx1-cosx

Q: Consider the equations of two planes. x + y + z = 0, 8x - y + z-5=0 (a) Determine whether the planes…

A: This question can be solved using the concept of angle between two planes.

Q: tim X-1 2 x² + ax +b = 2 find 9, and b a, X² + X=2

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Q: Find the cross product u x 7 where u = 2i -3j +k and = (7, - 3, 4). ü xü= Check Answer

A: We have u→=2i-3j+kor u→=2, -3, 1Alsov→=7, -3, 4

Q: Find the area of a triangle PQR, where P = (-4, -2,-2), Q = (-5, 2, 5), and R = (-2,5,-4) Check…

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Q: x Cothx Y = (Sink x) 4 Find dry" dx [ Sin'x]

A: Given: y=sin hxx cot hx

Q: Evaluate f(x, y, z) dV for the specified function f and B: JB f(x, y, z) dV = f(x, y, z) = Z x 2 ≤ x…

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Q: This is all one question. I really need help on this. Thank you so much

A: Given: peter goes on a ferris wheel that has a diameter of 36 feet and the distance fro the bottom…

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy(x,y) for the function f. f(x,y) = 5x e 5xy fxx (x,y) =…

A: The given function is: f(x,y)=5xe5xy

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7,…

A: To find out the position of the particle.

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: 1.5: The area of the region enclosed by the graph of f(x)=√x and the x- axis on the interval [0, 4]…

A: Area bounded between the curves : Consider the curve y=f(x) and x-axis on the interval a,b , then…

Q: 1261 (2x+1 dz 4-3x -x² 1 (((x+) dx (3) 28 (2x-3 dx √(x²-1) (2x+3) 31 32 33 dx √(x²+1) (2x+1) alx…

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Q: Consider lines L₁ and L₂. L₁: x = 1 + t, y = t₁ z = 2 + t, t€ R, L₂: x-3=y-1=z - 3 (a) Verify…

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Q: Using calculus, find the absolute maximum and absolute minimum of the function f(x) = 7x² − 14x + 4…

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Q: 4. Consider the vector a=(-2,3,-1). [ [K/U] Find the magnitude of the vector ä. b) Find an unit…

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Q: Differentiate the following function. You do not need to simplify the derivative. F'(x) = F(x) = 6e²

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Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

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