Find the area of the curve y = x² and y = 9

Q: Q3: Find the area of the region bounded by the curve y = x³ and the lines y = -x, y = 1. (Draw the…

A: Given problem:- Find the area of the region bounded by the curve y = x3 and the lines y = - x, y = 1

Q: Team Alpha was on their night patrol in Mystical Forest when they suddenly noticed that a flare was…

A: here distance we have to find  a = 9.8 v0 = 5 t = 5sec S=?

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Q: Q.1// (A) Use trigonometric substitution to find f- x²-2x-5 x3-5x² (B) Use partial fraction to find…

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Q: 2. A lifeguard standing at the water's edge sees a man flailing out in the water. She runs along the…

A: This question can be solved using the concept of trigonometry.

Q: → → If m= (2. 1. 5) and n = (3. 0. x) are perpendicular, then the value of x is

A: Solve the following

Q: - Find the derivative of f (t) = (5t³ — 4t² + 1) 49 f' (t) =

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = 1², y(t) = 2t, z(t) = ln t, t€…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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Q: Find the slope of the tangent line to the curve below at the point (5, 3). √x + 4y + /5xy…

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Q: figure out absolute min & max values: g(x)=cos^2(x)-3sin(x) Interval: 0<=x<=pi

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Q: 11. Oil is being pumped continuously from a Texas oil well at a rate proportional to the amount of…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) I COS(π/X⁹) dx X10

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Q: 2 . show that V(x,y) = x 'f (2x+y) is the general Solution of: av X du 2X 1 = V ду dx

A: To show that, vx, y=x f2x+y is the general solution of: x∂v∂x-2x∂v∂y=v

Q: Which of the following is a point on the plane with equation n = (-3, -2, 2) + t(2, 2, -2) + s(1,…

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Q: x²-5y²-3x-y +22=0 (y-2)(x-y-2) = 0

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Q: Set up the triple integral that will give the following: : 0≤ x ≤ 1,0 ≤ y ≤ (a) the volume of R…

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Q: mathematically

A: We will solve the problem

Q: (3x²2y²)y' = 2xy,when x = 0, y = -1

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Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

A: Given:a=-3i+2jb=2i+aj

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(8y) dy =…

A: Let's solve given diffrential equation.

Q: Find the length of curve x = t², y = t³ from x = 0 to x = 5.

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Q: Region R is a plane region bounded by the curve y = 32, the y-axis and the lines y = 1 and x = 4.…

A: We have to find the area and volume.   According to our guidelines we can solve only three subparts…

Q: Solve and illustrate the problem. 1. Find the volume of the wedge cut from a right circular cylinder…

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Q: Set up the triple integral that will give the following: 6. (a) the volume of R using cylindrical…

A: We have to set up the volume integral.

Q: hand written plz 1 5. Let D be the region bounded by the lines y = x, x=3 and the curve y = r (a)…

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Find the general solution of d²y dt² + dy + 20y=e-2t sin(4t).

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Q: For each of the following, find (i) the direction of P₁P2 and (ii) the midpoint of line segment P₁…

A: Given, P1(1,4,5)P2(4,-2,7) Therefore position vector of P1 and P2 is p1=i+4j+5kp2=4i-2j+7k

Q: [x²-1 x#1 x = 1 I. II. III. 7. Given f(x) = {*²2 f(1) = 2 (x+1)(x-1) A. I only B. Il only obrisani…

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Q: integral

A: Please refer to the image below

Q: What is the f(7) (-4) of g(x) = 2 205x53x¹ +9x³ +9² +2x+1 ? - 6 O 1/3 0 0 O-4 O 240

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Q: The width and length of a rectangle are measured to be 3 m and 5 m, respectively. These come with an…

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Q: [Select] the derivative of y? y = x⁹e²x+1 18. Which rule is applicable when solving for A.…

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Q: Evaluate y' y = cosh²12x +sinh²6x

A: To find out the derivative.

Q: Solve for y at x=2: (x5 + 3y) dx - x dy=0; x=1, y=2

A: Rewrite the differential equation in standard form and solve it

Q: Use Cartesian coordinates to evaluate JJ v² av where D is the tetrahedron in the first octant…

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Q: ¹In(1+x) -dx 0 X

A: Expand log series

Q: 4. Evaluate the double integral: y f. L y¹/3 x7 +1 (Hint: Change the order of integration to dy dr.)…

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Q: Consider the following vector fields: F = (3x²e²ª, 2x³e²y + 2 cos y sin y) and Ġ = (y+z, x+y, z —…

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Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A: To find out the population 3 years from now.

Q: 3. Let B=(2,4,6,8,10), C=(4,8, 10), and D= (xxis even). Answer the following questions. Explain (a)…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: By inspection, find the eigenvalues of the following matrix: Enter the eigenvalues in increasing…

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Q: Compute n Σ₁ tan(kx) tan((k+1)x) k=1 tan(nx) O a. + (n + 1) tan x b. tan((n+1)x) + tan x − (n +…

A: Trigonometric series

Q: 1. Evaluate a) for²dr, 2. Evaluate fr+7r² dr. 3. Evaluate a) fe²dr, r/2 4. Find sin rdr. b) dr, c)…

A: 1. evaluate  a) ∫01x2dx = [x3/3]01 = 1/3   b) ∫231/x2dx [-1/x]23 = -1/3 +1/2 = 1/6   c) ∫12x2dx =…

Q: Given the function f(x) = 5x(sin x + cosa) what is f' (4)? O No correct answer O -1.996 O -2.99 Ⓒ…

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Q: R, S and T are closed sets implies RnSnT is closed.

A: given

Q: If f(x) = 5x(sin x + cos x), what is f'(x)?

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