Find the average value of f(x) = Enter the exact answer. fave = x (6x² + 5)² over the interval [0, 1].

Q: Find the arc length of the curve below on the given interval. 3 1/3 3.5/3 y = 5x +9 on [1,27] The…

A: The given curve,    y=35x53-34x13+9 on 1,27

Q: 8 Find the sum of the series. Σ4¹/n-41/(n+1) answers. n=1 Give reasons for your

A: We have to find the sum of the given series.

Q: Using triple integrals, calculate the volume of the set in 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤z<5-x²-y² Ps:…

A: Find Volume of the set in 0&lt;=x&lt;=1, 0&lt;=y&lt;=1,&lt;=0z&lt;=5-x2-y2 .

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0,4, -3), and R=(-6, -1, - 5)

A: As we know that; The expression for the area of the triangle PQR is: A=12PQ→×PR→   Given: P=6,-3,-5,…

Q: determine the interval of increase (in interval notation) b) determine interval of decrease

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Q: If 1 1. f(x)dx = n(x) - tan(x) - 4² + x² + 6x + 0 4e C 3 then find f(x)

A: We can find f(x) as below, by finding the derivative.

Q: ¹(²+1) 3 lim (x + 1) sin( 24x

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Q: The derivative of a^u with respect to x is a ln a du/dx (a^u) * du/dx ln a * du/dx (a^u) * ln a *…

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Q: Determine whether​ Rolle's Theorem applies to the following function on the given interval. If so,…

A: Rolle's theorem states that if a function f(x) is continuous on the closed interval [a, b] and…

Q: (6xy - 3y² + 2y)dx + 2(x − y)dy = 0; when x = 0, y = 2

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Q: Approximate the area under the curve y = x² from a = 3 to x = 6 using a Right Endpoint approximation…

A: Follow the procedure given below.

Q: (a) [1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Q.1: Solve the differential equation below; xy' + 4y = 8 x¹

A: We have to solve above differential equations

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

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Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

Q: Is Wa subspace of the vector space? If not, state why. (Select all that apply.) W is the set of all…

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Q: Find the radius of convergence and the interval of convergence. xk k(k + 5) Radius of convergence:…

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Q: if f(x,y) = √x² + y + 4, then find a a21 and ах ду х

A: If fx, y=x2+y+4, then to find ∂2f∂x2 and ∂2f∂y∂x.

Q: For any two nonparallel vectors a and b, it holds that Select one: O O O 3a + b 3a + b 3|a| + |b|…

A: For any two nonparallel vectors a and b , it holds that

Q: Given the function f(r. y) = 1² + y² + 1 • For every point (r. y) = R², compute the gradient and the…

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Q: Represent the plane curve by a vector-valued function y=1-x^2

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Q: Determine whether the set, together with the indicated operations, is a vector space. If it is not,…

A: We have to choose correct option.

Q: Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for DNE…

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Q: O Question 1 A tank is filled with a fluid with density 71 ----- The cross-section of the end of…

A: Given the diagram of a tank. To find the total work to lift the fluid of the tank.

Q: lim h→0 (e) cos( 4 + h) h 1

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Q: 2 For the f(x)=2x² - 4x² defined -2≤x≤3 on the interval A. Find all critical points B. Find absolute…

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and b=. (a) Find the unit vector u…

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Q: Given that 2+i is a zero of f, find all other zeros. (Enter your answers as a comma-separated list.)…

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Q: The value of the definite integral [²3x²dx 3x² dx is Select one: 3 26 1 26 26 none of the others 26…

A: Solution is given below:

Q: Question Which of the following is a potential function f for F(x, y, z) = (2x cos(v2). -x²z sin(yz)…

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Q: Consider the graph of f'(x) given below. At what value(s) of x does f(x) have a local minimum? If…

A: we have given the graph of f(x) we know that at maxima and minima f'(x) =0  (means slope at that…

Q: Consider the function Find ¹(x), where is the inverse of f Also state the domain off in interval…

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Q: √y Find the mass and the center of mass of the lamina with density 8(x, y) = - x² +1 the rectangular…

A: Please see the below picture for detailed solution.

Q: Solve the given differential equation by undetermined coefficients. y" + y = 3x sin(x) y(x) =

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Q: [1 Q6: Find A1 where A = 3 2 -1 6 1 0 -2 4

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Q: The Maclaurin series of the function f(x) = 2x² sin(9x) can be written as f(x) = Σcna" 71=0 where a…

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Q: Convert the rectangular equation to polar form x² + y² = 9 (solve) rsin0 = 9 r=4.5 Option 4 O Option…

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Q: Find ln(9.2) from ln(9.0) = 2.1972 and ln(9.5) = 2.2513 by linear interpolation and get the %error.

A: We need to find ln(9.2)

Q: Find r'(t), r(t), and r'(to) for the given value of to. Then sketch the space curve represented by…

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Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(?) and y = r sin(?), and note that (x,…

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Q: True or False: Suppose k is constant. Then 5 [² is equal to 10k. Select one: True O False kdx

A: Solve the given intregal

Q: Find the equation of the curve at every point of which the tangent line has a slope of (1+y^2)/2xy…

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Q: Consider a continuous function f(x). The function has critical points at x = 0, x = 2, and x = 3.…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

Q: Find r'(t) r(t) = e-ti + 7j + 4teck r'(t) = (No Response) Need Help? Read It Watch It

A: Let's find derivative of given function.

Q: (a)i Find a vector equation and parametric equations for the line that passes through the point A(5,…

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Q: Use Green's Theorem to evaluate the line integral of F= over C which is the boundary of the…

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Q: Find the derivative using logarithmic differentiation. x(x+4) (5x + 1)(3x +7) y =

A: