7) x¹ 9-x ² dx X 3 2 2 where u-x ² dv = x √ 9-x² dx 2

Q: Determine wether the sequence converges, or diverges. If it Converges, S(2n-1)! 2(2n+1)!S

A: We have to find sequence converge or diverge..

Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all x ≤ (a,…

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Q: Given: parametric curve H defined by x(t) = tan¯¹t and y(t) = e¹t, where t € R (a) Find the slope of…

A: Given that parametric curve H defined by x(t) = tan-1t       and    y(t) = e4t , t ∈R           we…

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Q: y x3 - 2x*-5x + 2

A: Second Derivative Test : Consider the given function f(x) .Find Critical point , f'(x)=0 (say) 'c'…

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A: To determine whether the following statements are True or False.1 If cosh x=62, then sinh x=22.2 It…

Q: A product can be produced at a total cost of C'(x) = 500 + 100x2 + x³ dollars, where x is the number…

A: Given that; Cost function and revenue function.

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: Consider the position function s(t) = -4.9t +31t+24. Complete the following table with the…

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Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t == . — = dt

A: Given:ds/dt=10csc^2(2t) To find: solution at s=2 and t=π/4

Q: [* [b3 - 3 3 dy

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

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Q: ds Find the complete solution of = 8t³ √√s. dt

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Q: II. Consider the circle C1 : r = 1 and the roses C2 : r = cos 2θ and C3 : r = 2 cos 2θ, each of…

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Q: a. On a rectangular cartesian coordinate system, sketch the parallelepiped having the vertices (1,…

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: First we draw the curves, y=6-x2.y=x,y=-2,x=-2.

Q: Calculate the effective interest rate for each of the following nominal interest rates: a. 3.25%…

A: This question can be solved using the concept of effective interest rate.

Q: Find the area of the region bounded by the curve y=x²-3x²-x+3 and x-axis from x=-1 to x=2. (Note:…

A: To find the area of the region bounded by the curve y=x3-3x2-x+3 and x‐axis from x=-1 to x=2.

Q: Evaluate J (2a² y +9y³)dA, D is the region bounded by y www 33522 a. 5 O b. 4811 5 OC. None of the…

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Q: ND THE AREA BOUNDED BY THE = x(x-1)², y-AXIS, AND THE =12

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Q: Starts the domain, vertical asymptote, and end behavior of the function.  g(x) = ln(3x +21) + 1.5…

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Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: The table shows values of a force function f(x) where x is measured in meters and f(x) in newtons.…

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Q: Find the limit of the following sequence that the limit does not exist- or determine. {(₁ + + )"}…

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Q: Find a particular solution of =(x−1)² if y=-21 when x=-3. dx

A: dydx  = ( x - 1 )2   , y = -21, x = -3 we have to find particular solution of it

Q: Question Find the area A of the region that is bounded between the curve f(x) = 4 sin (4) g(x) = 4…

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Q: etan 4s | (cos (cos 4s)2 ds

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Q: a.) Solve the equation z³ − 1 = 0 15 1 √3 b.) Evaluate (-+-+3) " 2 2

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Q: Given: planes ¹: 2x - 5y+z=-1 and 2: x + 5y+z=5 intersecting on a line . (a) Determine the symmetric…

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Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 3

A: Given: x=y2+2y8-ln(y+1) The arc length is: L=∫ab1+dxdy2dy Now, dxdy=dy2+2y8-ln(y+1)dy…

Q: (a) f'(x) = -12 X = 0,-1 (b) f'(x) = 0 X = 1,-6 (c) f'(x) = 12 x = 252 X X X

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Q: Find the length of the spiraling polar curve r = 6e50 From 0 to 2. The length is

A: SOLUTION-

Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x-2).

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Q: 5. x x2 + x − 6 dx

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Q: Let P be the point with Cartesian coordinates (6,9), and C be the plane curve with parametric…

A: The parametric equation,x=t2-t and y=2t3-1123

Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 Cos 0 Er = g(0) = 12/250c4 D:r=3 (1.) Show…

A: Let's solve part 3 and 4.

Q: 18. What is the length of the polar curve below? 3πt x = 8cos (0) for 0 ≤ 0 ≤ ³1

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Q: 2-1 4s - 4 s² - 16/

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Q: 4. Verify the final value theorem for the function 3t²e-4t and determine its steady state value.

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Q: Calculate the volume of the solid of revolution generated by rotating the graph of the following…

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Q: Two payments of $8,000 and $6,100 are due in 1 year and 2 years, respectively. Calculate the two…

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Q: Solve the differential equation a. (4x³y² - 6x³y - 2x - 3)dx + (2x¹y-2x³)dy=0 b. (x-4y-3)…

A: If the differential equation Mdx +Ndy =0 is exact i.e, ∂M∂y=∂N∂x ,then solution is        ∫y…

Q: f(x) = 3 cos ((x − 4)) +32.

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Q: The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

A: Given, f(x)=x24(1-x)

Q: Find the area of the surface generated by revolving x=√(8y-y2) on the interval 2≤y≤5 about the…

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Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: The given integration is I=∫53+x2dx

Q: Problem 3. A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is…

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Q: Calculate the integral approximation S12 for Si ²1 dx. +1 S12 =

A: