A cylindrical container with circular base is to hold 64 in^3. Find its dimensions so that the amount (surface area) of metal required is a minimum when the container is a closed can.

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A: We will do second derivative test to find minimum area.

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Q: dx x²Vx² – 49 FOTE: Enter the fully simplified answer with no fractions under the square root and wi...

A: We will find the integral. 

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Q: Find the derivative of the function. PLEASE HELP ME ANSWER WITH SOLUTIONS

A: ddv1-2v1+v3  

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A: Here f(x) is not defined but at x=-2, x=3, x=5 .

Q: 1. Let f(r) = r' on [0,5). At r= 27, the Fourier series of f converges to (a) -27 (b) 27 (c) 8 (d) 0...

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Q: The Differentiation to be made must be based on the following topics. - Power Rule Give 3 examples w...

A: It is required to give three examples with solution and final answer on differentiation using power ...

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Q: Test the series for convergence or divergence using the Alternating Series Test. E(-1)"- + 5 n=1 Ide...

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about r = r, and then find the nth Taylo...

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Q: Select all vectors perpendicular to the vector (1,3, -5). (2, 1, 1) O (0, 5, 3) O (1, 1,3) O (4, 2, ...

A: Given query is to find the perpendicular vectors to the given vector.

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 3 %3D P4(x) ...

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Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

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Q: Let the height of an object bef(t)=t2+2t−4f(t)=t2+2t−4. What is the instantaneous rate of change of...

A: Given query is to find instantaneous rate of change of the object at t = 2.

Q: 1. Let E be the solid triangle in R³ whose corners are the points (1,0,0), (0, 1, 0) and (0,0, 2). C...

A: We have to compute the integral.

Q: Select all vectors parallel to the vector (1, –3, 5). O (2, –6, 10) O(-1,3,6) - 15 ? 5 )

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Q: Power Rule Give 3 examples with solution and final answer. Make sure it is unique and not advanced.

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Q: Find the derivative of the function. S(2) = VE - 8E f (x) =

A: topic - derivative of a function

Q: Use L'Hopital's Rule to evaluate the exact value of lim(x² – 2x+1)*-1.

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Q: d'y Find dz? of the function given implicitly: 6xy + 7e = 7e.

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Q: Determine whether the series is convegent or divergent. If it is Convergent, find its Sum, 8) nニ2

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Q: Consider the following sequence: (a,) = {n – n²} n-1 Use an+1 - an to show that the given sequence (...

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Q: A y' and Y"For Y=sin (X+ Y) 11 dar

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Q: Consider the following sequence: {a, } = {n – n² }= Use an+1 - an to show that the given sequence {a...

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Q: What dimensions will maximize the lateral surface area of an inverted cone, if V = 27 cm³?

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Q: 2. Find the derivative for each of the following, be sure to use proper notation and simplify when n...

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Q: Assume that a rectangle with sides x and y is changing with time. Let y = 2x and x(t)=t^2 What is t...

A: Given query is to find the rate of change of area.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Given query is to find the general term for the sequence.

Q: Determine whether the series converges, and if so find its sum. 00 k-D1 1) This series can be rewrit...

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Q: For each of the following functions, determine: (a.) the critical numbers of f (b.) all relative ext...

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Q: Use the Quotient Rule to find the derivative of the function. Re) = cos(e) f(t) f'(E)

A: Given f(t) = costt5wktduvdt = vu'-uv'v2

Q: XP If x=Y Vi-y!.find d

A: x =y1-y2 dy/dx = ? now derivate with x dx/dx = (dy/dx)1-y2 - (2y2/21-y2)(dy/dx) 1 = (dy/dx)(1-y2 - 2...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 k + 7 k(k +...

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Q: c) an (-1)" (4)" d) аn — 5 — п

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Q: Find the equation for a quadratic function that has horizontal intercepts at t = -2 and t = 5 and pa...

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: In this sequence, we will get the succeeding term by multiplying 1/17 to the preceding term. Such ty...

Q: Integration using Algebraic Substitution x²dx 1) S Vx+2 3

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Q: Fin d the intervals on which f (il I a creassing and decreasing are Con cave uP and con cave down an...

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Q: Determine whether the series converges or diverges. In(k) k k = 1 converges diverges

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Q: II. For each of the following functions, find the indicated derivative using the definition. Show so...

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Q: Suppose that > an is an infinite series with partial sum SN = 7 – n=1 N2 10 16 What are the values o...

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Q: Practice: Find the volume of the solids generated by rotating the area bounded with the given functi...

A: Question - a Given functions, x=y2x=2-y2 Axis of rotation, y=1 Formulas used: ∫xndx=xn+1n+1