1. Evaluate the iterated integral. (a) */2 sin 8 IT 00 */2 asine (b) ² dr de 0 rcos 0 dr de 0

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A: Let's solve given maximizing volume of a box problem.

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A: I am attaching image so that you understand each and every step.

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A: Derivatives

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A: We have to find the absolute extremum for the function f(x)=4x4-7.

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A: See this solution in below

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Q: Find the absolute extremum, if any, for the following function. f(x) = 4x+ -7

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Q: Applied Calculus Class: Please see the complet review example for reference. and solve the given…

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A: This question is based on application of integration.

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Q: 6. Find the area of the region bounded by x = y³ − 4y² + 3y and the x = y² − y. 77 (a) A= square…

A: The region is bounded by the curve x=y3-4y2+3y and x=y2-y

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Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m³/min. 3…

A: Given: Rate of inflow of water, dVdt=2 m3/min Height, h= 3m Radius, r=2m

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Q: solve the system of equations by Grammer Method. 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 2 x₁ + 2x₂ +…

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Q: a) [ Show that the equation 6x + 6y-6z + 3x² + 3y² + 3z² = 18 represents a sphere, and find its…

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Q: 5. Iny+ea²²x+y = 10 -

A: Given :According to given , only 5 solvedlny+ex2y2-x+y=10

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A: In this question we have to find the projection of the point on the yz-plane.

Q: In Exercises 101-108, assume that each sequence converges and find its limit. 101. a₁ = 2, an+1 102.…

A: The objective of the question is determine the limit of the given sequence.

Q: A gallon of milk is slowly leaking inside your refrigerator. The number of ounces in the container,…

A: The given data is: V(t)=128e-0.007t To find: How fast is the milk leaking from the gallon container…

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Q: Question 1 [ a) Find the value(s) of y such that the vectors U₁ = and U₂ = are parallel. b) Find…

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A: Given that,

Q: 2. Use root test to determine whether the following series is convergent or divergent: 00 (-1)" (In…

A: We have to find whether the series is convergent or  divergent by root test.

Q: 3. The Laplace transform of the f(t) = t²e-2t cos(3t) is (a) 2(+2)(8²+45-23) (s²+45+13)³…

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Q: Find the area of the region bounded by the curves, x = −6 ,  x = 6 , the x−axis  and the parabola…

A: Follow the procedure given below.

Q: 2. Find the first 4 terms of Taylor series for the function (In x4) about x = 3 ?

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Q: The following differential equation (+1)² + 2²/ x2 dy x² has an order of 02 3 01 = sin x

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Q: Q1.B. if k-1 is an eigen value of (2), find one corresponding eigen vector?

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