Evaluate d³yd¹y + dx5 dx4 - 6 d³ y dx³ = 0 =

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Q: Tim X+0¯¯ [(x² - In (x + 1)) cotx]

A: We have to solve useing L’Hôpital’s Rule

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Q: A) A retailer has been selling 1,000 computers a week at $750 each. The marketing department…

A: Please see the below picture for detailed solution.

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A: Graph :

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Q: Using Rationalizing Substitution a=4, b = 9 a = 8,b=27 a=64, b= 729 a=2, b=3 729 S 64 dx √x - √√x =…

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A: hhh

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Q: Using Rationalizing Substitution S- O In(y) + C O Arctan(y) + C O2Arctan(y) + C O2ln(y) + C dx…

A: ∫dxxx-1Substitute y=x-1→dydx=12x-1→dx=2x-1dy=2∫1y2+1dy

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Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

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Q: dx √x-3√x X ffv)dy, find fly)

A: solution:-∫64729dxx-x3dx=∫64729dxx12-x13dxlet x=y6 or y=x1/6x=64,     y=641/6=2x=729,…

Q: 1+x² 1. Find the area of the region bounded by the curve y=- 2x² and the lines y = 0, y = x, x = 2.

A: Given problem:-  1. Find the area of the region bounded by the curve y=(1+x2)/2x2 and the lines y =…

Q: 0 00 00 Consider the function f: (-2, 2)→ R defined by Mex X 6t D = S(x) = [₁ = [₁₁125²4d² - dt -…

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Q: Consider the function. x-7 f(x) x-6 Step 1 of 2: Find all values of x that correspond to horizontal…

A: solution:-f(x)=x-7x-6f'(x)=x-6ddxx-7-x-7ddxx-6x-62f'(x)=x-6-x-7x-62f'(x)=1x-62,     x≠6for…

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Q: Consider dx x1/2 + x2/3 Find the integrand in terms of z. A [62²dz 1+z² B none of the choices 6 z5…

A: Using rationalizing substitution

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Q: the sum of two numbers is 40. express their products as a function of one of the numbers.

A: Let's express product of two numbers as a function of one number.

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Q: In Exercises 1-3, find the solution of the given IVP. 1. d²y dy +4 dt² dt 5y = 0 2. y(0) = 11, y'(0)…

A: Please re-upload the other two questions.

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Q: Let f(t) 3t* Then f'(t) = 7t + 7e'.

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Q: dx Using Rationalizing Substitution S- -=Sf(y)dy, find ff(y)dy- X√√x-1

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Q: and the area of the plane region, 0≤x≤ bounded by y=sin x. x = ₁, and the x-axis- 2 O1s.u. S.U. 2…

A: We have to find area of plane