4. Prove that 473 1 (3n+1)³ 81√3

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A: given function is f(x)=2x3-42x2+240x-2

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Q: V3 4 dx (tan¯¹ (x)) (1 + x²)

A: ∫134tan-1x1+x2dx

Q: 6. Trace the curve: r² = a² (1 + 2 cos ) → (degrees) r Ⓒ (degrees) r → (degrees) r → (degrees) r…

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Q: 1 (s+1)(s+2) We have: L-¹{~ -¹ { Select one: O True O False -}=e=t+e=2t

A: To determine whether the following statement is true or false. L-11s+1s+2=e-t+e-2t

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Q: M8

A: Use the Ratio test

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A: Let two positive numbers x and y Given their product is 169 Let the sum of x and y is denoted by s

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A: We have to solve the differential equation.

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A: For a differential equation  ∫Mdx + ∫Ndy = 0 for differential equation to be exact ∂M∂y = ∂N∂x

Q: 31. The revenue from producing x units of a product is R = 12x 0.001x² (a) Find the additional…

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A: Sum= Σk=0∆xf(k)  =∆x(f(0)+f(1)+ f(2)+.....f(n-1))

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A: Let two functions u and v then ddx( u,v ) = udvdx + vdudxGiven function f( x ) = ( x2 + 5 )( 3x - 1…

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Q: -In ( + C) = n u' (x) = e6x-5u

A: Use seperate the variable

Q: 107 107 Suppose that a₁ = 9 and b₁ = -28. Compute the sum. i=1 i=1 107 Σ(1ai i-1 (1ai - 10bi)

A: we have given ∑i=1107ai=9   and ∑i=1107bi=-28

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Q: 59. Find the rate of change in the supply x of a product if the price is $150 and the supply…

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A: To find the equation of the tangent line to xt=6 sect, yt=6 tant at t=π4 in slope-intercept form.

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Q: 1 5 A 3 2 1 To find the blue shaded area above, we would calculate: [ f(x)dx = area Where: a= 1 2 3…

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