Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 3 + 2y2, 1≤ y ≤2

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

A: Derivatives

Q: hat's the derivative of y=15x cos x

A: Given: y=15x cos x To find its derivative

Q: Evaluate the integral 11 In (5) log 5x X dx = 11 1 In (5) log 5x X dx.

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Q: If 4x − 2x² <f(x) <x² - 2x +3 for - all real numbers except for x=1, then

A: We have to solve given Questions.

Q: T(x, y, z)= 1500e PQ y²-z² where T is measured in °C and x, y, and z in meters. 1. Find the rate of…

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Q: 2. Choose one question out of the following two questions. (1) Let A be the 3 x 3 matrix defined by…

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Q: Identify the open intervals where the function /(x)=x²-3x4 is increasing or decreasing. A increasing…

A: On solving this we will get

Q: Classify each differential equation as separable, linear, homogeneous, or bernoulli equation. Some…

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Q: . S(2y + 3)² √y+ 2 dy

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Q: Q5. What is if y = 300(3x) +7sin(2x)- 8x37

A: Given y = 3cos( 3x ) + 7sin( 2x ) - 8x3

Q: s of the tangent line and normal line to

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Q: If x² + xy + y³ = 1, find the value of y'" at the point where x = 1. I 23 X

A: Here we have to do differentiation.

Q: 4. dx cotx A) 1-sin xA (2 csc x-1\

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: on a family vacation amy's dad drove the car at a constant speed and traveled 585 miles in 13 hours.…

A: Given: distance= 545 miles time = 13 hours  New distance= 810

Q: Set up the integral that gives the area of the given surface. S= 27 4 S2 2T (2√9-y) 1+ 0 The area is…

A: To solve the given integral

Q: The shaded region between the graphs of y = −2x² + 20 and y = 3x – 15 is displayed below in - 25+ -6…

A: y=-2x2+20and  y=3x-15fot intercetion points  -2x2+20=3x-15

Q: For fin(3x²)dx. Part A: Rewrite the integral using substitution as the product of two functions in…

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Q: Find the derivative of the function using the definition of derivative. g(x) = = √9+ 2x g'(x) =…

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Q: 1. (a) Sketch the region enclosed by the given curves, including clear labels of all the curves, and…

A: Sketch of the region:

Q: Find e > 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

A: given y=x2-c2and y=c2-x2given area is 270

Q: The function f(x) = x³ + 7x² + 0x − 16 is graphed below. Plot a line segment = -6 and x connecting…

A: To find the values of c which satisfy the mean value theorem

Q: This question makes an important point: the maximum point of a function may not always be found by…

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Q: Is the derivative 15?

A: Given, y=15xcosx The derivative is y'=15cosx-xsinx

Q: The monthly revenue R (in dollars) of a telephone polling service is related to the number of…

A: Given revenue function:- Rx=-12000+203.5x2+15x

Q: The figure shows cost and revenue for producing q units. For the production levels in the table…

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Q: Differentiate. y' II y = et 7x²

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Q: 3. A 50-gal tank initially contains 10 gals of fresh water. At t = 0, a brine solution containing 1…

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Q: Obtain the differential equation of the family of circle with center on the x-axis ? a. yy" +…

A: Given center of the circle is on the x axis let center is at x= a so coordinate of center = ( a , 0…

Q: Evaluate Inx 10 X 7 In x 10 dx = x dx. (Type an exact answer.)

A: Given integral:- ∫1710lnxxdx

Q: Suppose that f(5) = 3, f'(5) = 9, g(5) = -4, and g'(5) = 6. Find the following values. (a) (fg)'(5)…

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Q: The cost, in billions of dollars, of airing x five-second hologram commercials during a Galactic…

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Q: ↑ sational Census Bureau predices that a cen population will chase 33. C in 2000 (a) Find an…

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Q: . Consider the function f: [1,4] → R defined by f(x) = x - √√x. A. What is the value of the signed…

A: Given: The given function is f:1, 4→ℝ defined by fx=x-x To find:  Find the value of the signed area…

Q: Show that In (x + √√x² + 1) = √√x² + 1² 1 & 1 . d_ \n(x + √ x² + 1) = x + √√x² + 1 dx d dx (

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Q: Assuming - 2x³ + 7y² - 9xy = 0 defines y as a differentiable function of x, use the theorem 기 dx…

A: Given -2x3 + 7y2 -9xy = 0

Q: answer

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Q: Evaluate the integral dx 9x log 5x dx 9x log 5x

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Q: 7.f(x) = 10x4 - 3x³ + 8x² - 4x - 8 8.f(x) = 4x5 + 3x² + 9x³ − 8x² + 16x - 24

A: Hi this is your answer.

Q: Rate of Change of Production Costs The daily total cost C(x) incurred by Trappee and Sons for…

A: The daily total cost Cx incurred by Trappee and Sons for producing  x cases of TexaPep hot house is…

Q: Consider the function f. Evaluate the following limit. D) Lim X²-2x+1 X-3 2)Lim X²-4 X-2 X²-5Xt6 3)…

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

Q: Suppose f(x) = { x² +1, x ≥ 3 2cx, x<3 Find a value of c so that f(x) is continuous at x = C.

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Q: Given selected values of the single number that could possibly equal the value of f'(7).…

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Q: Find the length of the unknown side of each triangle. Give the exact length and an approximate…

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Q: Which of the following is an ordinary, linear differential equation of order 2? +k²xt = 0 d²x +k²x =…

A: Find which equation is linear differential equation of order 2.

Q: √x-5 f(x) = x² 8x 20 Find the intervals of continuity of this function f(x). - - NOTE: Use 'INF' for…

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Q: A manufacturer wants to design an open-top box having a square base and a surface area of 150 square…

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Q: Which of the following have the same value sin x with lim? X x →0 lim x-0 lim 1 X-- lim x 0 1 sin (x…

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Q: If f is a differentiable function, then False True d da 1 = f'(x) f(x)²

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Q: Assume A = A₁ + A₂ and A, B = 0. If A₂ = kB, show that k = ● (5) (6) Use the formula x = r' (t)…

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Q: Find the derivative of the function. h'(x) = h(x) = √ 1 -X 2 1-x² √1-x² sin-¹(x) X

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