Hi I need help on solving this problem for my calculus: Evaluate the limit: lim x -> (3pi)/(2) (sin2(x) + 6 sin(x) + 5)/ (sin2(x) - 1)

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A: The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

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A: ∑k=1∞1k4

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A: f=&lt;-√6,-3√2&gt; Trigonometric form = ||m||&lt;cosθ,sinθ&gt; m=(vx2+vy2)tanθ=vyvx

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Q: (c) dx So ² (x² + 1)²

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A: NOTE: Refresh your page if you can't see any equations. . the given equation is and the given…

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Q: Find area of the region under the curve y = 4x³ - 2 and above the z-axis, for 3 < x < 8. area =

A: We know that the area of the function f(x) at x=a to b is  int_a^b f(x) dx

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A: The given function is: f(x)=4x-x2 ;          0, 4

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Q: . z = 12i + 16j

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A: The polynomial is given by x2+11 To determine: The expression of the polynomial in factored form.

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A: We know that the area formula int_a^b {f(y)-g(y)} dy

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Q: Find fif f'(x) = 2 + cos(x), f(0) = −5, ƒ(π/2) = −8.

A: Given, the information f''(x)=2+cosx, f(0)=-5, fπ2=-8. We have to find f.

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A: The function is Fx=∫-1x3x2-4x+7dx.To find : Find the equation for the tangent line to Fx…

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A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x the derivative is…

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A: x=y2-4 and x=18y4-y2+2

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A: Given :an=ln12n+2-9+4n

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A: The linear density function of a 1 meter rod is:ρ(x)=39(x+1)2  kg/m     for  0≤x≤1

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Q: (12) Describe each system of planes. If possible, solve the system. a) x + 2y + 3z = 4 2x = y + 4z =…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…