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Q: is satisfied. Finally, to determine if Rolle's Theorem can be applied, we also need to check if the…

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Q: Integral Calculus: Trigonometric Function (3

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Q: Graph the function. Show at least one period. 15) y = 2 sin (2ax - 3)

A: the graph for given function is attached below:

Q: csc ² 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. A True B)…

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Q: Solve

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Q: Q3) Evaluate triple integral , dz dx dy.

A: We can calculate this as follows:

Q: Suppose the demand for an item is given by the demand function,D(q)=−8q+580, where q is units sold…

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Q: 5. Evaluate f V2x + 1 dx. (2x + 1)/2 + C a. 3. b. (2x + 1)/2+ C c. (2x + 1)/2 + C d. (2x + 1)/2 + C

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Q: (-1)" V2n2 + 5 Given: power series > (x + 1)" n=1 ii. Find the interval of convergence of the power…

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Q: (x² + y³ )dx – –dy = 0 The equation ху Separable 1st order ODE Exact Homogeneous Linear

A: Solving

Q: A company produces two types of solar panels per year: x thousand of type A and y thousand of type…

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Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

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Q: x< +2 dx 1. I (x – 2)(x² – 2x +2)

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Q: Question Consider the function f(x) below. Over what open interval(s) is the function decreasing and…

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Q: Determine if the improper integral converges or diverges. Find its value if it converges. Show…

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Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

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Q: (a) Find the first partial derivatives of the function f(x, y) = x²yVy + 4y². %3D (b) Find the…

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Q: Determine whether the following functions below is a solution or not a solution of the integral f(1-…

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Solve if the improper integral below diverges or converges. If it converges, solve for the value. 1…

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Q: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: The concentration of a drug t hours after being injected is given by C(t)=0.8t / t^2+68. Find the…

A: This question can be solved using the concept of maxima and minima.

Q: -ions of the line through (-1, –2, 5)

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Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: What is the particular solution of the equation 2ydx - 3xdy = 0 when y=1 and x=1?

A: Solving the differential equation by seperation of variables.

Q: Find the second-order partial derivative fry (x,y) for the function, f(x, y) = 4x3 - 5x?y-3y + 9

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Q: 2 Vy x+j Q3) Evaluate triple integral S dz dx dy х-у

A: We can solve this as follows:

Q: Given the following heat equation and the boundary and initial conditions, и, 3 би,и, и(0,1) 3…

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Q: Find the length of the polar curve r=2cos(theta) 0 < theta < pi

A: Given:         r = 2 cos θ        0 &lt;  θ &lt; π

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7,…

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Q: ...................... Consider the following. 4 f(x) = (a) State the domain of the function, all…

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Q: 10n? + 18 7n2 + 16n + 21 n=1

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: For the series below. (a) find the series' radlus and interval of convergence. For what values of x…

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Q: (b) / Vx² – 4 dx

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Q: (-1)"x2" (2n)! COS X = for all x € R. n=0 1. Let f(x) = cos(Vx). Determine the power series…

A: I have solved all three questions.  Hope this will help. Please upvote ?

Q: Identify if the following series is convergent or divergent: 00 (-1)"3n² 4n2–1 n=1

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Q: given below, evaluate lim f(x) and lim x→-00 f(x) = -4x² + 2x +4 sin (9x) ses without bound, you…

A: We have to find the following conditions according to the given information

Q: e1/n n2 n=1

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Q: Evaluate triple integral ſ´, S,2 ¯* dz dx dy .

A: We can solve this as follows:

Q: A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P…

A: We have to find co-ordinate of P

Q: Question For the function given below, which statements concerning Rolle's theorem are true? 4x + 3…

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Q: Section 6.2 p. 558/560 # 70 In the following exercises, express each series as a rational function.…

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Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: Let g be a differentiable function of x, and let the range of g be an interval [a, b]. Let f be a…

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Q: Find the volume of the given solid over the indicated region of integration. f(x.y)%3D4X+5y+7;…

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Q: Consider a, = for n EN = {1,2,3,...}. 2n +1 2n +3

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Q: Problem 1 (а, Find the first partial derivatives of the function f(x, y) = x²yVy + 4y2. (b) fxyx of…

A: fxx,y = ∂f∂x  ;  fy(x,y) = ∂f∂y. fxyx(x,y) = ∂∂x∂∂y∂f∂x

Q: Question A 5-foot ladder is leaning against a wall. If we push the ladder toward the wall at a rate…

A: let x be the distance of bottom of ladder from the wall andy be the distance between top of the…