Find the exact length of the polar curve. r = 3 cos(theta),    0 ≤ theta ≤ pi

Q: 10 A particle is moved along the x-axis by a force that measures pounds at a point x feet from the…

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Q: Set-up the integral for the area A(R) of the region R bounded by the circles y2 + x² = 4, and y2 +…

A: Region bounded by two circle in fourth quadrant

Q: A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f…

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Q: Sketch the curve with the given polar equation.

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Q: Find the solution to   x′=y y′=12x+4y   if x(0)=0 and y(0)=5.

A: we have to solve system of differential equations

Q: Find the volume of the solid generated when the region enclosed by y = Vx, y = 12 – x, and y = 0 is…

A: Follow the procedure given below.

Q: aluate the triple integral zdV, where E is bounded by the cylinder y? + z? = 9 and the planes a = 0,…

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Q: A cable 200 ft long and weighing 4 Ib/ft is hanging vertically down a well. If a weight Of 100 lbs…

A: Given

Q: For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

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Q: Compute f′(x). a) f(x) = (x2 +1) e−x^2  b) f(x) = (4e−x − e−3x)3  c) f (x) = x2 ln (x2 − 4) d) f…

A: Product Rule of differentiation : du.vdx = u.dvdx +dudx.v dxndx=n.xn-1 deaxdx=aeax Note : As per…

Q: True or False: If lim f(x) = 4 and lim g(x) 3, then %3D %3D lim[-3f(x)² – 49(x)] = -60 O False O…

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Q: For each problem, find the particular solution of the differential equation that satisfies the…

A: The given differential equation is: dydx=exy2 ; y-2=2e3+3e3e   As we know that; The Power rule:…

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

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Q: Eliminate the parameter to find a Cartesian equation of the curve with parametric equations x = e^t…

A: Just put the exponential term value from one equation into the other and easily eliminate the…

Q: Evaluate the triple integral / z dV where E is the solid bounded by the cylinder y? + z2 = 441 and…

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Q: Write each pair of parametric equations in rectangular form. Then sketch the curve. 8) x= 4cos t+ 1,…

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Q: Work Problem 1 (a) Sketch the surface generated by revolving the line y = x/2, 0< x < 6, about the…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: Given: z=0z=x2x=0x=3y=0y=3

Q: (e) Compute y' if y2 = xe + ye-

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Q: f(x) = = hen -6x I+3 f'(3) =?. (Answer accurate to 2 docimal

A: Given f(x)=-6xx+3f'(x)=ddx-6xx+3…

Q: Find the solutions of the system of inequalities by graphing: ¤ + y 2

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Q: d'y If 4x2 + y = 40 then evaluate when = 3 and y = 2. (Answer accurate to two decimal places.)

A: Topic = Derivative

Q: Let f(x) = Va and g(x) = x² – 1. Find go f and determine its domain. |3D %3D

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Q: Simplify arcsec2.

A: Given,             arcsec2To find : Simplify

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

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Q: Q1 (- Use the comparison test to verify that the following series converges: 1 n =17+n6

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = Va2 – x2 R…

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Q: Find the area of the shaded region. (2,7) (0,3). 26 2/3 2/3

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Q: Find the directional derivative of the function at P in the direction of v. F(x, y) = x³ - y, P(8,…

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Q: -The magnal cost of a produt is modeled by , uhen x-(5, C=40. Find the cost functon.

A: Given query is to find the cost function.

Q: Solve the initial value problem  y" + 8y' + 25y = 0 ; y(0) = 1, y'(0) = 2

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Q: x4 - 4x3 + 4x2 + 1 2. Determine the open intervals where the graph of f(x) is concave upward or…

A: We can solve this as follows:

Q: Use the comparison test to verify that the following series converges: 1 Σ n=15+n7

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Q: 4. Find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x) over the…

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Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: Use herons formula for finding the area of triangle

Q: yA (b) Economists study two functions: R(1) and C(r) which are the revenue and cost when r units of…

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Q: (a) Suppose that f is differentiable, positive and decreasing on (a, b] and has no critical points.…

A: Given problem:-

Q: tch the vector field with its graph. F(x, y) = yi y 事 5 -5- -6+ y 1信 I 5 5 -5+

A: Given  F(x,y)=yi Option (1) is correct by given graph

Q: Find the area of the shaded region. r = Vcos 20 r = 10 cos e NOTE: Enter the ezact answer. A =

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Q: A ALEKS - J'Angello Farrington X Messenger www-awu.aleks.com/alekscgi/x/lsl.exe/1 0- う O EXPONENTIAL…

A: Here we are given a function which is defined by the following rule  f(x)= (1/4)-x And gor different…

Q: lim, 1 f(x) = %3D

A: limx→a f(x) =L if and only if limx→a- f(x) = L =limx→a+ f(x) .

Q: Simplify tan( arccos ). V3 O1 V3/3

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Q: Jse Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: For the graph of y = f(x) shown to the right, find the absolute minimum and the absolute maximum…

A: The absolute maximum of a given graph is the point on the entire graph with the highest y-value…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (6,…

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Q: QUESTION 1 Find the magnitude and direction of the vector acceleration when t=2 seconds for an…

A: Position vector:r(t)→ =t3, 1-t2Velocity vector:v(t)→ =r'(t)→ =3t2, -2tacceleration…

Q: x²-x dx 1+3x²-2x³ 2-2x3

A: Given problem:-

Q: 1+3" 5. E 00 By the series test: n=1 2.

A: By Ratio test the given series diverges. Now, what the Ratio test is Suppose we have the series ∑an.…

Q: _9. Which of the following is equal to fo°dt? A. e C. ex+C D. et +C B. e° +C _10. What should be the…

A: Given data÷