Determine the instantaneous rate of change of the function √ sin sin (2³) f(x) = [x² x3 At x=1 dt 1+√t

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A: A detailed solution is given below.

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Q: 3. Solve the differential equation of order one.  y' = csc x - ycot x STEPS: a. Put the equation…

A: Integrating factor of a differential equation of the form, dy/dx +P(x)y=Q(x) is given by, I.F=…

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A: To evaluate the following definite integrals using the Fundamental Theorem of Calculus.c ∫164t-1t+t3…

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A: We have to find the integral.

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A: The diagram of the cylinder with hemisphere on the end will be as following To find dVdr at r=2,…

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A: A detailed solution is given below.

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Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

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Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: π 2 EK 4 cot4 x dx

A: Here, note that: ∫cot4x dx=∫cot2x cot2x dx=∫(cosec2x-1) cot2x dx=∫cosec2x cot2x dx-∫cot2x…

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

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A: Evaluate the integral

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Q: Evaluate ²(2x + 3e* - 1) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given problem:-

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Q: 1. Solve the differential equation of order one. Show your solutions. y' = x - 2y STEPS: a. Put…

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Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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A: To find for what  values of r the given term becomes solution of differential equation.

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Q: Find the area in square units bounded by the following: (Show graph and detailed solution. Box final…

A: Here, the area bounded by the curves: y=x3+1 and x-axis  with the limits x=0 and x=3 is:

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Q: 2. Find the area of the region bounded by x=y², x=-1, y = 2 and y = -1.

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A: As we know that the parametric equation of ellipse at a point acosθ,bsinθ  is given by…

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A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…