Perform the integration. (sinh x)(coth x +csch3x) dx +

Q: Sketch and set up integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13…

A: Please see the below pictures for detailed solution.

Q: Find the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)

A: Given: points (0,1,3), (2,2,2), (3,2,1) Find: equation of the plane containing given points

Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

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Q: C. Find the slope and the equation of the tangent line to the curve. 23. y 2x−x+2 at (-1,5) 24.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

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Q: Perform the integration. 3 (13 (|3* − 1| + |3* − 3|) dx 0

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Q: The Philippine Postal Service will accept a box for domestic shipment only if the sum of its length…

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Q: C. Find the slope and the equation of the tangent line to the curve. 21: y=x²-4x+1 at (2, -3)

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: (Requires a short but nontrivial geometric argument.). Let ABC be a triangle with angles…

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Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: The solid generated by x+y=5, y=0 and x=0, about y=0

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

A: Here we have to find the volume.

Q: Find the linear approximation of the function g(x) = 1 + x at a = 0. g(x) * Use it to approximate…

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Q: (b) lim *+1 √√2x+6-2 x²-1

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Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

A: Given

Q: 3x² - 6x² + x (36²-6x² x)]d² X

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, R'(x)=(x+2)ln(x+2)

Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: 0<x (x^L - x)x = (x)ƒ

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

Q: Evaluate the improper integral or state that it diverges. Ĵ 5dx Select the correct choice below and,…

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Q: Perform the integration. x-1 S= dx x² + 5x + 8

A: ∫1x2+a2 dx =1atan-1xa+C

Q: Problem Revolve about the (a) x-axis and (b) y-axis the area enclosed by y² = x and y=x³.

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Q: 7. A particle moves along the x-axis with its velocity modeled by the function (t)= 3cost + 3t. The…

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Q: Find all points where the function has any relative extrema. Identify any saddle points. f(x,y) =…

A: f(x, y) =4x2+6xy+3y2-4x-8 In this question, we need to find all the points where the function has…

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: Q) choose one only 1) If y = (x − a)√/2ax − x² + a² sin-1 (*), then y' = 2√/2ax-x² - a a is…

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Q: You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

A: This question can be solved using the concept of maxima and minima.

Q: Given Cost and Price (demand) functions C(q) = 110q+40000 and p(q) = -2.6q + 800, what is the…

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Q: II. Evaluate the following integrals. 4. J 9x² 9x → 5 - 18x + 13 - dx

A: A detailed solution is given below.

Q: Use implicit differentiation to determine the derivative of: tan² (xy² + y) = 2x.

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Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Let x and y be the dimensions of the rectangular field. According to given , Area(A)= xy= 4000…

Q: evaluate lim x →0 sin x-x 3 x

A: Given, limx-&gt;0 (sin x -x)/x³ SInce we have a indeterminate form, Applying l'Hoptials rule we…

Q: Read and understand the problem carefully. Show your solutions. 1. The Basco Lighthouse has a…

A: Concept: Trigonometric functions: Circular functions, normally referred to as trigonometric…

Q: Test for exactness, then solve.  ey dx + (2y + xey) dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: topic- quadratic equations and derivatives

Q: Given that Inx+3 f(x) = 3lnx-1 Find the formula for f−¹(x). State the domain of f−¹(x). Show all…

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Q: The amount of a certain substance in a chemical compound is given by the function C (t) = 20.6…

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: Find fx(x,y,z), fy(x,y,z), f₂(x,y,z), and fyx (x,y,z) for the following. 3 f(x,y,z) = 4x³ + 2xy -…

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Q: The total cost of producing 1 unit of a product is given by C(x, y) = 80+ 0.3x² + 50y - xy dollars…

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Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

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Q: Inventory Microbucks Computer Company makes two computers, the Pomegranate II and the Pomegranate…

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Q: Find fx (x,y) and f, (x,y). Then, find fx(1, -2) and fy (-3,3). f(x,y) = -2xy +9y² + 10 fx(x,y)=

A: We can find the answer as below.

Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: 4. Let sinx = Ź (-1)" x²n+) 2n+1 n=d ♦ a) Find a paver series for xsinx, Differentiate the power…

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Q: What is the y=x^2 4 and O 1/4 01/2 1 3/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: Convert the degree measure to radian measure. Round to three decimal places. −46.23°

A: Convert the degree measure to radian measure. Round to three decimal places. −46.23°   Please show…

Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

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Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

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