Find y': y = arc cos 0 = -√2 O y Oy=-1/72 V Oy= Oy=-- 9-1² 3

Q: Find the domain of the vector-valued functions: R(t) = √t² - 9 î+ In]t − 3] ƒ + (t² + 2t − 8) k B.…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Given the demand function D(p) = 400 - 2p², Find the Elasticity function E(p) Find the Elasticity of…

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Q: Given the points A: (3, — 2, 2) and B: (5, 2, 6), find the vector u = AB

A: The points are given by A3, -2, 2B5, 2, 6 To evaluate: The vector u→ = AB→.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: solution:-the region bounded by 27y, x=0 and y=3 rotating about y-axisusing cylindrical shell…

Q: Evaluate the following integrals using substitution(s): Might want to use your own paper 1. S - x²…

A: According to guidelines we can solve only first question .solution:-(1)∫x31-x2 dxlet 1-x2=t,…

Q: Sketch the level curve of the function z(x, y) = x² + y² for c = 81.

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Q: Jse logarithmic differentiation to find the derivative of the f 3x y =(√x) ³x ''(x) =

A: We need to find out the differentiation of the function.

Q: 3. a) For what values of p is the integral cl sin b) In th x(In x)P da convergent?

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

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Q: 5. List all critical points of T(0) = sin² 0 - cos 0 for 0 ≤ 0 < 2π.

A: Find all critical points of T(θ)=sin2θ-cosθ for 0≤θ≤2π.

Q: 27-30 Compare the values of Ay and dy if x changes from 1 to 1.05. What if x changes from 1 to 1.01?…

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Q: r(t) = (0,8 cos³ 10t, 8 sin³10t), ≤ t ≤ 4

A: I am attaching image so that you understand each and every step.

Q: and x³ and y = √√√x. Find the area enclosed between the curves y = x³

A: We can find the area between the curves.

Q: Which of the is the best transformation of f trigonometric substitution? Of sec 0 de Of 5 sec 0 de O…

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Q: 2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the…

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Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4321 per…

A: The given data is: A population of particular yeast develops with a constant growth rate of 0.4321…

Q: Solve x + (3x + 1)y=e-3x dx Select one: O a. y = xe-3x + ce-3x O b. y = e-3x + cx-¹e-3x O c. y=e3x +…

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Q: f(x) = 3x4 cos(x)

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Q: Find the values of v such that g'(v) = 0. (Enter your answers as a comma-separated list. If an…

A: Given function  g(v) = v3 - 48v + 8

Q: Tutorial Exercise Find the derivative of the function. HINT [See Example 1(b).] h(x) In[(-3x + 7)(x…

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Q: Finally, f(x) = 5(x2-9). Practice Give an expression for f(x) using only Real-valued coefficients,…

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Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in…

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Q: Solvex - y = x² sinx dx Select one: O a y= cx? − xỉcosx O b. y = cx+xcosx O c. y = cx-xcosx Od. y=…

A: Topic = Differential equation Correct Option  = c

Q: Find the standard equation of the sphere that has the point (1, — 6, 2) and (3, 5, 6) as endpoints…

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Q: Find an equation of the level curve of the function z(x, y) = ey (x² + y2) that passes through the…

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Q: Find the limit. lim sin(3x) X-0 2x

A: To find the following limit.limx→0 sin3x2x

Q: A farmer has 100 feet of fence with which he plans to enclose a rectangular pen along one side of…

A: Given query is to find the dimenyfor maximum area.

Q: Find the limit. 3 - 3 tan(x) lim x→→/4 sin(x) - cos(x)

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Q: Evaluate: fx In xdx X ○ 25 (In x-²) 5 25 (In x-1) 5 + C O 25 (In x+²) 5 + C O None of these + C

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Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: 1 X √√√1-x² dy dx 0

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Q: Find the following for the given equation. r(t) = (et, 7+², 5 tan(t)) (a) r(t) = (b) r(t) = (c) Find…

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Q: Given the function x³ + y³ = 4, find y' Oy = = Oy = = 0 y = = V Oy =

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Q: Let a = (9,5) and 6 = (5, -3). Compute the following vector projections. proja b projz a =

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Q: Find Cross Product Find the cross product u x 7 where u = 6i +8j +8k and 7 = 6i +8j +8k and 7 = (4,…

A: Topic = Vector

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 9 assuming that a(9) =…

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Q: 7. f(x) = 0.2 sin²x - cos 2x, 0≤x≤ T

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 1. The graph of f on [0, 10] is shown. Use it to answer the questions. Write NONE if necessary. Y 5…

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Q: 47-48 Simplifying a Difference Quotient Simplify using the 1101 Binomial Theorem. (x + h) ³ - x³ h…

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Q: Find the differential of the function f(x, y) = x√y at the point (2, 7) using Az = 0.3 and Ay = 0.15…

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Q: A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another…

A: Topic -Mean Value theorem We are given, Initial speed of car =0mi/hr Final speed of car= 60 mi/hr…

Q: 4. f(x)=2", a = 0

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Q: 6x g(x) = -5x8 + (a) | 19 (1) a (b) 1 g(a) (c) g(√a)

A: Given query is to perform indicated function operations.

Q: Find the derivative of f(x) = 5√√x - - 7 28 Type your answer without fractional or negative…

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Q: Jsing Linear f(x) = ln (x), a = 1, Use decimal notation. Give your answer to two decimal places.) Af…

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Q: Find sec 0 if tan 0 sec A Get Help: Video - 15 8 and cos > 0. Answer exactly. eBook Preview TIP…

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Q: Find the solutions of the following IVPS or DE. a. y" — 4y' + 4y = e²x, b. y" - 2y = e2²x +3, y(0) =…

A: See the details solution in below

Q: Find the constant of integration of the first order linear differential equation ydx + (1 + 2y^2)xdy…

A: Let's solve given diffential equation.

Q: Find the Laplace transform of the function. -t f(1) = 1²e-¹ A B C 24 s5-1 There is no correct answer…

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