It can be shown that the polar curve r = a sin(0) +b cos(0), where ab + 0, is a circle. Find the center (in Cartesian coordinates) and radius of this circle in terms of a and b. x-coordinate of center: y-coordinate of center: Radius:

Q: Let L be the line r(t)=(1+1,1-2r,3+5t) and II be the plane 2x-y+3z-48=0. a Find the point of…

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Q: find the flux of 3 – e")i+ (y³ + sin z)j+ (z³ – unded above by z = V4 – x² outward orientation.

A: We have to find the flux using the divergence therom according to the given information

Q: Let T: R - R be a linear transformation such that T(1, 1, 1) = (4, 0, -1), T(0, -1, 2) = (-5, 4,…

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Q: Given s(t)= 21+21, where s(t) is in feet and t is in seconds, find each of the following a) v(1) b)…

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Q: Use Stokes' Theorem to evaluate F- dr. F(x, y, z) = xyi + x*j+z?k where Cis the intersection of the…

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Q: Let g(t) give the total number of gallons of maple syrup sold by a local farmer over the first t…

A: The derivative is defined as an instantaneous rate of change at a given point. g(t) gives total…

Q: 10. Given two points P1(0,2,-1) and P2(2,0,-1), find the perpendicular distance from the point P3(3,…

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Q: Let y = 5x?. Find the change in y, Ay when x = 2 and Ar 0.4 Find the differential dy when a = 2 and…

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Q: 8 Evaluate for (3x² -7x+4

A: We have to use the concept of derivatives

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Q: (235 – 4.x25 + 2x)dx

A: The detailed solution is given below Thank you

Q: (3x-2)cx In the integration --17 what integration method is appropriate? a. Integration by Power…

A: Use integral methods

Q: y'= x(5-x)² when: Theni I y=0 y=0 x: 0 (0,0) Use vertical element metho d: y x(5-x)*

A: Given question is solved with explanation.

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Q: Compute f, for f(x,y)=xln(xy). %3D

A: We can find the answers as below.

Q: x dx 2 /9 – 4x²

A: Using integration

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Q: evaluate the region S

A: answer is in next step

Q: Suppose that f is a function given as f(x) = - x² +x – 2. Simplify the expression f(r + h). f(x + h)…

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Q: Find f+ g, f- g, fg, and fig and their domains. F(x) = V15 - 2, g(x) = Vx+1 Find (F+ g)(x). Find the…

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Q: Calculate ri(t) r2(t)] and [ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: Let's find.

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x312 from (0, 0) to (4, 8)

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Q: Integrate the square root of sin (In x) dx * O x/2 [ sin (Inx) + cos (Inx)] + C x/2 [ sin (Inx) -…

A: Given

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Q: Use Green's Theorem to find the work done by the force field F(x, y) Vyi + Væj on a particle that…

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Q: Find all the values of x where the tangent line to the function f(x) = x° - 8x - 6x +2 is…

A: For horizontal tangent line dydx=0 Given :

Q: 1 Answer: diverges n In n n=2

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Q: a) Find the arc length of the catenary y = coshx between X 0 and x = In4. b) Graph the functions y =…

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Q: The distance a biker has traveled after t seconds can be modeled by f(t) feet and f(50) = 64. f'(t)…

A: f'(t) > 0 imply function increase with time.  f"(t)< 0 imply function is concave downward

Q: Verify the formula LF a ds = S cdiv F dV in the Divergence Theorem by evaluating the surface…

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Q: Provide an appropriate response. Find f(n) if f(t) dt x sin 8x.

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Q: Find the derivative of y(x) = In (8(In(x))'). (Use symbolic notation and fractions where needed.) dy…

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Q: Write the equation of a sine or cosine function to describe the graph.

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Q: In the integration of (cos x)^4 (sin x)^3 dx, what is the appropriate transformation? O Transform…

A: Solving the problem by finding the perfect transformation.

Q: Find f such that f'(x) = f(4) = 20.

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Q: Question 3 z+3 dx Use the substitution u = 1 - 2. 1 O sec I|+3 sin x+C OIn(1 – a) + 3 sin-1 a + C…

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Q: The exact area of the region enclosed by f(x) = -(x+ 2)(x-2) and g(x) = (r+ 2)(x- 2) is given by…

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6…

A: Given problem:-

Q: -1 Solve (1 1 using the inverse of a matrix. 1 6.

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Q: A company that produces cell phones has a cost function of C = 6x² – 197x + 1859, where C is the…

A: C= 6x2-197x+1859differentiating w.r.t xC'=12x-197+0C'=012x-197=0x=19712

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: First we will draw graph for function.

Q: Determine an equation of the line tangent to the curve Y = 5x-4 at the point with x- coordinate 4.

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Q: II 2. 3. 2. 4. x² 1. X. 3. D3x 4. 1. Find the given derivative. 4-part 1 Homework: Homework Chap

A: Dx3x-12 + 4x32=Dx3x-12 + 4x-32                               =3Dxx-12+4Dxx-32…

Q: |A:k||2||Br:||2) < ||A||F||B||F k=1

A: answer is in next step

Q: -2000x has the marginal-demand function D'x)= where Dx) is the number of units sold at x dollars per…

A: First we'll integrate and the we'll put the given value. So i am providing my handwritten notes…

Q: Sketch the region enclosed by Y 6x and y = 9x". Find the area of the region.

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Q: initial deposit of $1,000 is placed in a savings account with an APY of 4.3% sume the interest rate…

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