- The region trapped between y = 4x 2 2x² and y = 2x² 1³ is shown below. - I

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: 9) Two apartment tenants have a total of 600 feet of fencing to enclose a rectangular garden and…

A: Given: Total length of fencing = 600 feet We know that area of a rectangle is length × width

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Q: Find the volume of the solid that is bounded by the cylinder z = 4x2, on the sides by the cylinder…

A: Let's find volume of solid.

Q: Consider the function f(x)= = x² + 7x + 12 -2 a. Find the first derivative. f'(x) = b. List any…

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Q: A piecewise function is defined as f(t) = {4,5 t 0 ≤t <3 t≥3 i. Sketch the graph of f(t). ii.…

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Q: i) n=1 1 1+2+3++n j) 1 n In n(ln(Inn)+1) k) 2" +n n!+1 n=1

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Q: Water is flowing into a conical cistern at the rate if 8 cubic m/min. If the height of the inverted…

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Q: dt 1³ +1²-2t

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Q: calculate the area of that part of the surface z = 2xy which is bounded by the planes   x+y=1, x=0,…

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Q: 3. Set up the iterated double integral in polar coordinates that gives the volume of the solid…

A: We have to find the volume of the given in polar coordinates.

Q: (b) the volume of the solid B that lies above the cone z = 3r² + 3y² and below the sphere x² + y² +…

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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: y = In (cot 8x)

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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: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…

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Q: o an iterated triple integral in the order dxdzdy that gives the vol first octant enclosed by the…

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Q: S 7. Evaluate 8. Evaluate 9. Evaluate (cos x - sin x) dx cot²x dx (sin x + x) dx

A: Given problems:- Solve the following using the theorems on differentiation. 7. ∫ (cos(x) -sin(x) dx…

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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: Test for convergence/divergence, State the theorems used.

A: As per guidelines, I can answer only one question. Since questions are not interlink with each…

Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over…

A: Explanation of the answer is as follows

Q: Problem 4. (. Let C be the curve given by parametric equations y(t) = 2t, z(t) = lnt, t€ (-∞0, +∞0).…

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Q: Determine the constants c and d in the equation of the curve y = ax + b³ + ca+d having a critical…

A: The objective of the question is determine the value of c,d on the given curve.

Q: 2. Evaluate da da d. Java [. 2 / + 3 + a r/Mr | 1 | dr ar/rº +1

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

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Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Q.2// Find (A) f sin¹ (x) cos5(x) dx (B) f 4t³-t²+16 t t² +4 dt (C) Use improper integral to find ²…

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Q: integral

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Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

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Q: Find the eigenvalues of A² for Enter the eigenvalues in increasing order. Eigenvalues of A² are: i A…

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Q: con 2. 體 + dt +13y = 3sin(2t)

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Q: o classify the following PDES :- 227 ахг <-2 822 буду +2 82 дуг =x+3y 2 X •x2 Ихх - 2 xу Иху +ў Иуу…

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Q: As shown in the required readings or videos find the general solution to the differential equation…

A: Here we have to find the general solution of the given differential equation,  y'+2y=2ex…

Q: sketch the graph of fox) = 2 1+x²²

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Q: Find a differential equation that corresponds to the given direction field. Consider differential…

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Q: Let f(x)=x²-4x²+3x and g(x)=4x+3 then find the product. Discuss the steps

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Q: Without using a calculator, compute the sine and cosine of 210° by using the reference angle. What…

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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€…

A: To find equation of tangent line and then arc length of thegivencurve.

Q: EXAMPLE: (0,0) 3x-2y 26 5x+45 O > 5 x a 1915 CRITICAL POINTS -A (30) ( B (2.0) 1 D ( ¾/5,9). ✓c…

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Q: A rocket is fired vertically upward from the ground. The distance in feet that the rocket travels…

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Q: A certain drug is being administered intravenously to a hospital patient. of the drug enters the…

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Q: Evaluate y' y = cosh²12x +sinh²6x

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Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х u(x,c) =4е 2 (зу-2х)12 ans3- и(x,…

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Q: Are Lebesgue integrals always finite?

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Q: x² - 5y²-3x -y +22=0 (y-2)(x-y-2) = 0

A: Given

Q: Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following…

A: I have just use the methods and easily find the all solutions. Main solutions are in the boxes.

Q: Using trigonometric substitution in integrating sqrt (x^2 - 49), the adjacent side is equal to?

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Q: A Norman window is in the shape of a rectangle surmounted by a semi-circle. 38. Which of the…

A: We are allow to solve one question at a time.if you need rest of solution please upload it…