Find the volume of the solid obtained by rotating the egion bounded by y=x+1₁ y=0, about y = -1. y = 0, and x=2

Q: The cylindrical shell method is to be used to compute the volume of the solid generated by revolving…

A: Here, the given curves are: y=2x-x2 & y=0 The area bounded by the curve is:

Q: Find the derivative of the following using the differentiation rules. (x²-2x) (In x³-3 tan x) x√x y

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Q: If the product of two positive numbers is 300, Minimize the sum of the second number and thrice of…

A: To find out the numbers.

Q: The numerical value of the lim n+3 nln (2) "→ ∞ \ 11 + 1 is equal to

A: We need to evaluate the value of the following limit limn→∞n+3n+1nln2 Formula Used: limx→∞1+axx = ea

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A: The objective of the question is evaluate the definite double integral.

Q: Consider the vector-valued function R(t) with Ả'(t) = (sec²(t − 1), - 2 Vt (a) Find R(t) given R(1)…

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Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: We need to find equation.

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A: We have to solve given Questions.

Q: Q2: A company plans to update its equipment so that its trucks are replaced after ten years from…

A: To find out the amount that company needs to pay each year.

Q: Sketch the graph of the function f(x): = 2x-3 x²-4

A: The function is  f(x)=2x-3x2-4

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: Topic:-  application of integration

Q: Find fy for the function f (x, y) = yx³ – 2x²y³ y - y³ x³ - 6x²y² Option 3 y - 6xy² 3 _ 2xy® -…

A: Topic:- application of derivatives

Q: The value of x for which the series Σ- O A. x<2 or 4<x. OB.2<x<3 or 3<x≤4. OC.2<x<4. O D. 2<x<3 or…

A: Given

Q: 3. Stan tan³ 3x sec ¹ 3x dx

A: As per our company guidelines, we are supposed to answer only one question. Kindly post other…

Q: 2. S 2 tan x secx - tan x d.r

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Q: Find the derivative of the following using the differentiation rules. x3 +6√x-7x+3 f(x) =

A: In this question, we need to find the derivative of the given function.

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: 5. Given the Standard Equation the DE, Identify the roots * d²y d³ y dx³ dx² + dx - 2- m: 1+ √2,0…

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Q: what is the final answer? can you write the final answer in 7/6 leters/min?????????? whats that?

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Q: Given the function f(x, y, z) = x ln(1 - z) + and simplify your answers. a) fa b) fxz sin(x - 1) 2y…

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Q: Sketch the graph of the funcuon f(x) = 2x-3 x2-4

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Q: Find all points on the curve y = x³ + 2x² - 6x + 5 where the tangent is parallel to the line 2x + y…

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Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element.

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Q: integrate * S(4√r – V√r² – 6√r³) dr 8 ·12 3 r³ – 2/4 r ² + C 5 35 r-ri-24r + C ² 35 24 3²-5r³+²+ C…

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Q: Consider the spherical equation given by p sponding equation in Cartesian coordinates. 4 cos sin o.…

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Q: Consider the region on the 1st quadrant bounded by y = √√4x²,x and y - axes. If the region is…

A: Using shell method, given format is obtained. From this format, evaluate m-n.

Q: Write an equation for the function graphed below. The y intercept is at (0,-0.5) 5 1 -7 -6 -5 -4 4 y…

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Q: Evaluate the following double integral over the given region R. JS Ta 4 ln(y + 1) (x + 1)(y + 1) dA…

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Q: Which of the following equations can be derived from the partial fraction decomposition of a…

A: We can solve this problem as follows:

Q: Consider the region on the 1st quadrant bounded by y = √√4 — x²,x and y - axes. If the region is…

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Q: Find the equation of the bisector of the acute angle formed by the lines 1+2y=3=0 and 2x+y-4=0. 0 a.…

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Q: The volume of y = (3x+1)+,x=0, x=8,y=0 O (28/9) TL O (26/3) T O (1372/9) O (248/9) m 6 and x = = 2y

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Q: Which ONE of the following statements is FALSE? OA. If the function f (x,y) is maximum at the point…

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Q: Using √√x + 1 √x-1 express the final answer in terms of X. Substitution Rationalizing dx = y² + 4y+…

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Q: √√2₁ y = ¹, y-axis, y=1&y=3; OY

A: Volume of solid obtained by revolving region around y axis is evaluated.

Q: Not yet Simplify 3-3-1-3-2 O a. 5(3-2) O b. none of these Oc. с. 3(53-2) O d. 33-2 o e. 3³-n

A: To simplify the given expression .

Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: f sin 3x cos 5x dx ¹29 sin 3x cos 5x + cos 3xsin 5x + C 16 sin 5xcos 5x + C O. 16 sin 3x cos 3x + O…

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Q: The graph of f(0) = -2cos(10) the graph of the function f(0) = 4-2 cos A 2π units to the left; 4…

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

Q: A closed wood storage having a volume of 27 in.3 is to be in the form of a right-circular cylinder.…

A: Volume of cylinder is πr^2h

Q: The cylindrical shell method is to be used to compute for the volume of the solid generated by…

A:

Q: Find all solutions to the given equation. In the choices, k runs through all integers. √3csc(x)+2=0…

A: We can find the answer as below.

Q: 3. Let R(t) = (t²,1 — t², t) and r(t) = cost. Determine the parametric equations of the line tangent…

A: Given

Q: Set up the integral representing the area of the region between the curves x = -1, x = 4, y = 2x -…

A: Consider the figure

Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

A:

Q: Which ONE of the following statements is TRUE with regards to lim (x,y) → (0,0) sin (xy) x² + y²

A: The correct answer is option D.

Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: First we find revenue function from given data.  And then we find maximum revenue for sold…

Q: boy wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the aximum possible…

A: Given query is to find maximum possible area.

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A: