Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

Q: Find the indefinite integral. (16x +13) In (2x)dx Select the method of integration that should be…

A: Integration by parts ∫udv=uv-∫vdu

Q: 1. Evaluate L²S³ (2y³ + x²y) dx dy

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Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A: To find the volume of the solid of revolution formed by rotating about the x-axis the region bounded…

Q: A bacteria culture initially contains 1000 bacteria and is growing at the rate of N' (t) = 2tt-2/3…

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Q: yı y' = 2x +2y +1 3x +y -2

A: We can solve the given differential equation .

Q: B. Find the derivative of each of the following functions. 14. f(x) = x² + 5 3x + 2

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Q: What is the exact value of sin(255°) +sin(195°)?

A: find value of  sin(255) +sin(195) here this is trigonometric function  lets find value of this

Q: sin(7) 8 What is the exact value of Show your work for full credit.

A: Given sin7π8 sin7π8=sin-π8+2π=-sinπ8Find  sin ( π8 )  by using trig identity:cos 2 a = 1 − 2 sin2 a…

Q: A Consider triangle ABC drawn in a circle of radius 6 cm with vertex C at the centre of the circle,…

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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: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Explained below

Q: valuate £₁² (2x + 3e* − 1) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23

A: We will solve the problem.

Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

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

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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: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: Determine whether the series k=1 3\k-1 converges and if so, find its sum.

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Q: You deposit $2000 in an account with 3% annual compound interest. Complete the following, assuming…

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Q: 2. A cyclist applies a force F with magnitude F = 50N in the same direction as the vector b = 4 j.…

A: We have to find the vectors.

Q: Solve the equation: (D² - 4) (D+2) y = 0 Oy=c₁e²x + c₂x²x + c3e-²x Oy=ce+exe + c3e

A: To solve the given differential equation.

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: Find the dimensions of a rectangle with area 1,728 m² whose perimeter is as small as possib m…

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Q: Your farm encompasses 900 acres, and you are planning to grow soybeans, corn, and wheat in the…

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Q: 3. SET-UP the definite integral that will give the area of the region specified using (a) z as the…

A: topic- area bounded by curves

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: x = 1. 2. Find the derivative of f(x) = 3x² - 5x at x = 1 using the formula f'(x) = lim f(x)-f(xo)…

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Q: Evaluate fx² cosh x dx

A: To evaluate the integral.

Q: Evaluate efffxv xdv,where D is the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

A: Given problem:- Evaluate  ∫∫∫D xdv ,where D is the tetrahedron with vertices (0,0,0), (2,0,0),…

Q: cos sin-cos -d0

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Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function

Q: In Dollars Sales Monthly 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 January Williams Custom…

A:

Q: 3. coth 3x dx

A: To evaluate the integral.

Q: The population of a city is 50,000. The city grows continuously by 2.2% per year. If this trend…

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Q: termine the absolute maximum and minimum values of f(x) = cos²x-cosx the interval 0≤x≤ 2π.

A: Please refer to the image below

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: 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: 0<x (x^L - x)x = (x)ƒ

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

Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: Question 8 A manufacturer has determined that the total cost C of operating a factory is C = 0.5 x²…

A: At what level of production will be average cost per unit

Q: A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics…

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Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: 3. Use the cross product properties to prove the relation (a - b) × (â+b) = 2(â × b) given a = (1,…

A: Given,a=i-3j+2kb=-2i+0j+k

Q: 3. Find f'(x) if f(x)= 3 2x + sin r

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Q: f(x) = x²+3x x+3 "2"⁰ 24

A: Since you have asked multiple questions in a single request we would be answering only the first…

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

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Q: 54. Look for the volume of the solid produced by rotating the region enclosed by 1792# T y - x² =…

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Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

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

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: Solve for the area bounded by the graphs of y = √√√x + 2, y = x + 2, x = 2, x = 4

A: Graph: