8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥ 0. Graph the resulting equation

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Q: Find the marginal average cost function if cost and revenue are given by C(x) = 190 +3.6x and R(x) =…

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi +…

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Q: Test the series for convergence or divergence. Select the correct answer. The series is convergent…

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Q: 2) [3 Solve the IVP: y" - 6y + 8y = 0, y(0) = 0, y' (0) = 2.

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Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

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A: Solution is given below:

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Q: Use implicit differentiation to find y', and then evaluate y' for x²y - 3x³ + 8 = 0 at the point…

A: We have to find out derivative

Q: etermine whether the work done along the path C is positive, negative, or zero. O positive O…

A: To find the work done along the path c.

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: Consider the integral a = • 9₂ (y) 9₁ (y) 9₁(4) = f(x, y)dxdy b = 64 *** f(x, y) dyda. Sketch the…

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Q: 10. Determine whether the series converges or diverges by using the integral test: Σnt n=1

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Q: when

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Q: (9x - 8) dx || +C

A: Solution of given question is written in below steps.

Q: 1) 3 Use reduction of order method with y₁(x) = e³x to find a second solution y2 for the DE: y" - 9y…

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Q: a) f, if any. Let f(x, y) = 2x² + 2y² - 3xy - 2. Find the local maximum and minimum values and…

A: The given function is: f(x,y)=2x2+2y2-3xy-2

Q: √x dx for n=4 is equal to Using Simpson's method 0 Blank 1 (use 2 decimal places with proper…

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Q: 7. Given r 2 sin(0) for T/2 ≤ ≤ 3π/2. = (a) Graph the region described above. (b) Using basic middle…

A: Given data÷ r=2sinθ ,π2≤θ≤3π2   a) The graph on the interval is a circle and is given below

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Q: Find the derivative of the function f(x) = (3x4-22³ - 10) ³/2 ○ f'(x) = (12x³ – 6x²)° ƒ' (x) = -—-…

A: The given function is f(x)=(3x4-2x3-10)32 We have to find the derivative of the function

Q: Evaluate the integral 2-x 2 [²² 0 0 xdydx.

A: Solve the integral ∫02 ∫02-x x dy dx. Concept used; Power rule of integration; ∫xndx=xn+1n+1+c

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Q: L3Q11.The number of bacteria in a certain food is a function of the food’s temperature. The number…

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Q: The demand x is the number of items that can be sold at a price of $p. For x = p2² - 4p +600, find…

A: We can solve as follows

Q: Evaluate: lim- A. 1 B. e C. 0 D. DNE E. ∞ →2+ [(x² − 4) (-2)]

A: We know, ln(ab)=b*ln(a)

Q: Find the average cost function if cost and revenue are given by C(x) = 164 +8.9x and R(x) = 3x…

A: Given;  C(x)=164+8.9x R(x)=3x-0.07x2.

Q: Solve the length of the unknown side. Round each answer to the nearest tenth. 13 19° 22

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Q: 2. Differentiate the following: (a) y = x²z

A: The given expression is: y=x2x   ...1   As we know the Product rule: f·g'=f'·g+f·g' The Power Law:…

Q: The double integral 0 Select one: True O False 2 √x has triangular region. f(x, y) dy dx

A: We can solve as follows

Q: Which of the following is the critical point of the function f(x, y) = x²y = xy? - Select one: ○…

A: The given function is: fx,y=x2y-xy To calculate the critical point, we have to solve the equations…

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Q: For the function f(x) = sinx, where a = find the following. 6 a. Find the Taylor polynomials of…

A: Please see the below picture for detailed solution.

Q: (a) Find the volume of the solids generated by revolving the region bounded by the curves y = 4-x²,…

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Q: A $5,500 bond that carries a 3.00% coupon rate payable semi-annually is purchase years before…

A: We will find the required.

Q: L4Q10.The first term of an arithmetic sequence is 11 and the second term is 16. Find the common…

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Q: Question 5 (a) Find an equation of the curve that passes through the point (0, -2) and whose slope…

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Q: Is the following statement true or flase? Select one: True False 5 2 1² 1²0 2 5 = √ √ ² x dx) ( √ ²…

A: The objective of the question is evaluate the double integral and choose the correct option.

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Q: (a) Find the volume of the solids generated by revolving the region bounded by the curves y=z²+1,…

A: To solve the following problem of finding volume using washer method.

Q: If f(x) = 4x + 14, find the slope of the secant line between the values of *₁ = 9 and ₂ = 2.

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Q: Find the derivative of the function f(z) = √2 O None of these. 37 Of(z) = √2z f(2)=

A: We will find the derivative.

Q: Find the volume of the given solid region in the first octant bounded by the plane 10x + 8y +20z =…

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