Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

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Q: 100 (e) Σ199 2i(i3 – 1) i=1

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Q: (a) For a certain curve, y"=2. Find its equation given that it passes through P(2, 6) with slope 10.…

A: Note: according to the company policy we can attempt only one question so please upload the next…

Q: Given that R' (t) = 2ti — 2j + 3t² k and R(2) = i + j — k, then R(t) =

A: The objective is to find R(t).

Q: 3. You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

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Q: Test for convergence / divergence. Find the limit if result is convergence.

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines

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

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Q: I. Determine the convergence of each of the following series using the indicated test. In number 4,…

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Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±7), vertices: (0,…

A: We have to solve above hypobola question

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

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Q: f(x) = 4√√x + 2x¹/2 - 8x-7/8 +x². f(x) +2 1 x3 = ²325/2 - 2x³/2+1/32²³- x³ - 2x² + x −1. 9

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Q: Convert the rectangular equation x2 = −2y2 + 5x2 y2 to polar equation

A: The rectangular equation is x2=-2y2+5x2y2

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: 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: 1. Use Comparison Test to determine the converges or diverges of the series Σ: 8 n=1 (n+1)√n

A: By using Comparison Test to determine the convergence or divergence of the series ∑n=1∞ 1n+1n.

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: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: In a certain country, the number of people who drive electric vehicles can be mod the function P(t)…

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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: Calculus Use the Table of Integrals to evaluate the integral. 1₁ 21²6 2t²e-t dt

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

Q: 9. ✓ (at x = ()) (at x=-2) 10. ✓ 2 (for all values of x) (at x = 3) 8.

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Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x + 4) in the interval…

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Q: Classify the following ODE's with respect to order and linearity. a. 3x-y' - 5y = 7x³ - 8x+1

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Q: - 4. Find the area bounded by y = x - x² and y = x(x − 2)(x+2).

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Q: The cost to produce a certain commodity is given by the function C(x) = 50x + 2,000 The…

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Q: 3. fx²(9-x³)5 dx 4. J√4x-1 dx

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Q: The production output of a certain factory is N(t) = √² + 10t + 8 where N(t) is the output in…

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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: 5. A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

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Q: What is the y=x^2 - 4 and O 1/4 O 1/2 01 03/2 Ο ΝΑ x-coordinate of the centroid of the plane region…

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Q: Payton is making stuffed animal keychains out of yarn. She set up an Etsy page to sell her keychain…

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Q: 10x-3y For the function f(x,y,z)= 8z + 1 fx=0 find fx. fy. fz, and fyz-

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Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.8q +800, what profit can be…

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Q: . A family wants to build a fence in their backyard for their dogs, but the cost for the previous…

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

A: Given: Now,     v(t)=f'(t)      =-16t2+286t+10'       =-32t+286

Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: IVICCE dy Find from the following equations dx Problem (iii) x³ + xy = 0

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Q: What is the component form of a vector with a magnitude of 17 and a direction of 125°?

A: To find the component form of the vector whose magnitude and direction are given.

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Q: The function defined by y=√-² has as its graph a semicircle of radius r with center at (0.0) (as…

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Q: Evaluate the following integrals. Show the solution. 1. fcsc² (7x + 5) dx 2. x² sec (4x³ +9) dx dx…

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Q: Give the Taylor series of the function f(x) == 1 3x²

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Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: Suppose that the number of crates of an agricultural product is given by 11xy-0.0002x² - 5y Z= 0.03x…

A: Suppose that the number of crates of an agricultural product is given by z=11xy-0.0002x2-5y0.03x+4y…

Q: For the function f(x,y) = √y² + 5x², find f(2, - 5), f(− 1,2), f( – 3, – 5), and f(0,9). f(2,-5)=…

A: Given query is to find the value of the function at indicated points

Q: Given Cost and Price (demand) functions C(q) = 120q+40000 and p(q) = -2.4q+800, what profit can be…

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