A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function 3000 x² where x is the price per unit, in dollars. Find the demand function if it is known that 1005 units of the product are demanded by consumers when the price is $3 per unit. D'(x) = - D(x) = or

Q: is said to be the Laplace transform of 7, provided that the integral converges. (()). (Write your…

A: We have to find the laplace transform of given function.

Q: H.w: Find the LT of the following functions: 3-f(t) = cosh at cos at

A: Given, f(t)=cosh at cos at

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Q: Please show your answer to 4 decimal places. Suppose that f(x,y)=e^(−x^2−2y^2−y)then the maximum is

A: We have to find the maximum.

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Q: The region bounded by f(x) = - 2x² + 8x + 24, x = = 0, and y = the volume of the solid of…

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Q: Which among the choices is not true about the continuity of f(x)? f(x) == O lim = +00 O f(4) is…

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Q: The marginal average cost of producing x digital sports watches is given by the function C'(x),…

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Q: Find the differential of the function f(x,y)=−5x√yf(x,y)=-5xy at the point (8,2)(8,2) using…

A: Concept: The value of dz and ∆z is given by  dz=∂f∂xdx+∂f∂ydy∆z=f(x+∆x,y+∆y)-f(x,y) Here ∂f∂xand…

Q: 3. Classify the graph of the equation as a circle, parabola, an ellipse, or a hyperbola. (a) 16x² -…

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Q: 11. Find L-¹ {F (S)} for each function: (a) s²F (s) + SF (s) — 6F (s) = (b) F (s) = (c) F (s): s 1…

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Q: estion 2 Find the directional derivative of the function g(x, y, z) = xye at P(3, 5,0) in the…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 35a. Use long division to derive the first four non-zero terms of the Maclaurin Series for f(x) =…

A: The required Maclaurin Series for the function f(x)=tan x are: 1.  sin x=x-x33!+x55!-x77!+x99!-...…

Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

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Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: Σ 500(1.07)" ΕΞΟ

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Q: Find ▼ · (V × F) if F(x, y, z) = 8 sin xi + 8 cos(8x − 9y)j + 10zk. V · (V × F) = [

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Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

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Q: The area of the finite region enclosed by the curves y = 3x² and y = 21 x is given by the definite H…

A: We will use definite integration to find the area

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Q: Find the AREA of the region bounded by: y = √√√x+2, y=x, and the x A. B. C. D. 37 6 19 6 10 3 16 3 F…

A: Topic = Area

Q: 4) A cylindrical coordinates equation for the cone z² = ²+1/² is: a. z² = 97² b. 9z=r c. 9z² = 7² d.…

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Q: Find f'(x) if f(x) = arcsin ve 0 f(x) = 2√1-2² 2√√√1-e 0 f(x)=√√² E² 21-e 1

A: Topic = Derivative

Q: 15. Find the volume of the solid enclosed by the surfaces 2 = 0 and 2-16-2-², whose projection onto…

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Q: Evaluate: lim, __.—3 (√22² — 10) (2²+x-6)

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Q: Verify the identity. (Simplify at each step.) 3 cos(x + y) cos(x - y) = 3 cos(x) - 3 sin²(y)

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Q: Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile…

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Q: Find the indicated nth partial sum of the arithmetic sequence. a₁ = 13, 316, n = 120 120 =

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Q: T 45-50. Binomial series a. Find the first four nonzero terms of the binomial series centered at 0…

A: 49. The given function fx=1+x-23

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A: Given: r(t)=etcost,etsint,et

Q: A first order differential equation involving current i in a series R-L circuit is given by: di/dt…

A: Laplace transform

Q: Evaluate the definite integral. (Round your answer to three decimal places.) *In(8) ex dx 1 + e²x

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Q: quotient rule of differentiation: d TC(y)) Y A MC(y)y-TC(y) ACADE ² ways positive the sign of the…

A: Here we have to explain how the equal sign in the red box indicate.

Q: Prove Vf(r) f'(r)r r

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Q: 1 rastr L²s² 2,2

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Q: 12. Find the integrating factor for the following equations making them into exact equations: 1.…

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Q: a f'm f(x) dx for the function f(x) graphed below. [Hint: No calculus is necessary-just as we used…

A: We can find the value of integral  of a function f(x) by using the area under the curve f(x).

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = xªcos x, n = 2, C = T

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Q: Use implicit differentiation to find y² + 8x³ = 3y - 4x² dy dr

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Q: Evaluate the line integral curve C : x = 4 cost, y = 8 sint (0 ≤ t ≤7 < NOTE: Enter the exact…

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Q: 3) Let D be the region enclosed by the two paraboloids z = 4 + x² + y² and z = 10-x² - y². Then the…

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Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &amp;…

Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: Given vector valued function:- rt=13t+1i+1tj Determine the interval(s) on which the given…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. (₁)-[ = T T r(t)…

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Q: Question 4 Which among the choices is not true about the continuity of f(x)? if x 1 -{₂ f(x) = x²,…

A: I am attaching image so that you understand each and every step.

Q: Is the answer to this question 2pi.

A: To explain that the given answer is correct or not.

Q: 4. If x= sin² and y = 1 when x = 0, then find the value of x when y = 3. 0 O 8 None of these

A: Topic- differential equation

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: A tank contains 300 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram…

A: Given problem:- A tank contains 300 liters of fluid in which 10 grams of salt is dissolved. Brine…