Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk between the point (1, -1, 0) and (e², -1, 1)?

Q: Use the chain rule to find, where First the pieces: End result (in terms of just t): dz = dt 江 西 | z…

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Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

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Q: The bacteria in a certain culture increase according to dN/dt = 0.25N. If originally N = 200, find N…

A: Integrate the equation.

Q: Questions 1-4: The graph of a function y = f(x) on the interval [-3, ∞) is shown below. Use the…

A: Given.

Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

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Q: Find the area between f(x)=1/x and the x-axis for 1≤x≤10, 1≤ x ≤100, and Is x ≤A. What is the limit…

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Q: It is projected that the population of a certain town will be P(t) = 2t+4+³/2 + 5000 where P(t) is…

A: Rate of increase of population=P(9)-P(0)9-0

Q: S 1 V1 + v 2

A: We have to find integral

Q: Given that -3 9+x² following functions: (-1)n+1 32n+1 4x (9+x²)² Σn=0 2. g(x) = x2n. Obtain the…

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Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

A: In this question, we want to differentiate the given expression implicitly.

Q: 5. [7.6] If vectors ū=(5,2,-1) and = (2,-1, 3) then... a) determine u x v. b) Explain the geometric…

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Q: Find T,N and k for the curve: 1- r(t) = (6 sin 2t)i + (6 cos2t) j+5tk.

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: The population of a city is 145,000. It declines continuously by 3% per year. ..... Assuming this…

A: Solution-

Q: Evaluate the following limit lim (3¹6) (²-√²+₂) Ꮳ X-4 -64 Show all your work. Warning: You will get…

A: Limits

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: Determine the area of the region bounded by x=3+y^2, x=2-y^2, y=1 and y=-2. *

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Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: To find the dimensions that minimize the amount of metal needed to make the can.

Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

Q: After t months on the job, a postal worker can sort L(t) = 700 – 400e−0.5ť letters per hour.…

A: answer is in next step .

Q: Find the area of are a the region i) Sketch the ii) Determine the boundarien iii.) set-up the…

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Q: Solve using Variation of Parameters (D² + 1) y = tan x O y = c₁ cos x + c₂ sin x − cos x ln(secx +…

A: The objective is to find the general solution using variation of parameter.

Q: Sort St Question 2. Evaluate the following integral region). Show all your work! cos(x²) dx dy. Make…

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

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Q: Evaluate fx² cosh x dx

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

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Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: Evaluate the following integral: a.) SIS z ln y tan z dV if S = {(x, y, z) = R³ : − 1 ≤ x ≤ 0, e ≤ y…

A: S is a rectangular cuboid, hence limit of each individual are independent so the integral are…

Q: III. Directions: Find the derivative of the given functions with respect to x using the limit…

A: i) f(x)=3x2+5x-7ii) fx=12x2-9x

Q: Find T,N and k for the curve:

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Q: You start driving away from Morgantown at 12:00. Your distance away t hours after you left is given…

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

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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: 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: A farmer wants to fence an area of 6 million Square feet in a rectangular field and a divided in…

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Q: ular bird sanctuary with one side along a straight river is to be constructed so that it contains 72…

A: Please refer to the image below

Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 71/6 81/5 91/4 62/3 None of…

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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: Convert the Cartesian coordinate (-1,-4) to polar coordinates, 0≤ 0 0 Enter exact value. 0-

A: Given, (x,y)=(-1,-4)

Q: 2 Find the area bounded by the parabola y = 4x and the line y = 2x - 4.

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Q: cos (+h)-cos(3) COS h I {+h)- - 3 3 h 3. Evaluate lim →(7/3) COS 4. Evaluate lim ₁0 π Cos

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Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

A: We have to find the area of the given region.

Q: A company produces a special new type of TV. The company has fixed costs of $496,000, and it costs…

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Q: Evaluate the following integral. JJ. xyz dV if S is the region bounded by the cylinders x² + y² =…

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Q: For the following function, find the equation of the tangent line at the point (1, 2). f(x)=√9x² - 1…

A: We have to find equation of tangent line

Q: As part of a chemical experiment, a scientist determines that the number sodium in a chemical…

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Q: A company produces computers. The demand equation for this computer is given by p(q) = -5q+6000. the…

A: Given the demand functionp(q)=-5q+6000where q represents the number of units:total Revenue…

Q: 1. A farmer wants to fence in a field and divide it into four side by side, equal areas. If he wants…

A: From the given data And, xy=8000&f(x,y)=2x+5y is the parimeter to minimize.

Q: y''-5y=sinx

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Q: Given m = 6, n = 1, and v = (-4, 7), what is v(n-m)?

A: Given :- Given m = 6, n = 1, and v = <-4, 7>, what is v(n-m)?