solve the problem with the second partial derivative test or with Lagrange's method: Find the volume of a rectangular box with maximum volume if the surcafe is 96cm2 please show full and complete procedure HANDWRITTEN only

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A: formula for surface area is  A=2π∫aby1+(dydx)2dxy=2x-x2dxndx=nxn-1

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A: The given problem is solved below in detail.

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A: The expression is given as log3(2x+27) = 5

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Q: Consider the graph of the function f(x) = Provide your answer below: x² 6x - 27 x² + 3x - 4 What are…

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A: Given query is to find quarterly payment total amount deposited and interest earned.

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Q: (2) ) (A) Suppose Ris the region in the second quadrant bounded by the circle x² + y² = 9, the lines…

A: Given that:- Region R bounded by x2 +y2=9 ,y=-x and x=0 in second quadrant

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A: Derivative

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A: According to bartleny guidelines we supposed to do the first one of multiple questionskindly repost…

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Q: = 9 to x = 15. Find the area of the region under the graph of f(x) = e-*/³ from * = O e (e-1) O e 5…

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Q: Simplify and write the trigonometric expression in terms of sine and cosine: 1 + cos y 1 + secy

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Q: Evaluate ftan a x sec4 xdx. +C

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Q: Evaluate the integral [x³√x² +2 √x³√x²+2dx = + 2 dx.

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Q: If where f(x) = c is a real number, then which statements are true? Select all that apply. O f'(x)=0…

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Q: Find equations of tangent lines to the curve y= Oy=-x-2, y = -x- 0 y=-x--, y= O y=-x-6, y=-x-²/7/…

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Q: 2 A 2401 5t +13 e that an automobile's velocity starting from rest is v(t) ation at 9 seconds. Round…

A: Given query is to find the acceleration at indicated point.

Q: 3. ff (zex² + y²) dv S with S bounded by x² + y² = 4 for 2 ≤ z ≤ 3

A: we have to evaluate  ∫∫∫zex2+y2dV  with  bounded by  x2+y2=4 for  2≤z≤3using cylindrical coordinate…

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Q: If y = f(x) then which of following expressions represents the derivative of the function with…

A: Given query is to find the correct options for derivative.

Q: Use l'Hôpital's rule to find the following limit. 1 In (x-7) lim X→8* lim +8²-X (2-3-1 x-8 G 1 X-8 1…

A: As we know that: The Power law: ddxxn=nxn-1 The product rule: f·g'=f'·g+f·g' The Quotient rule:…

Q: If f(x, y, z) = x - y³ + e² and r(t) = ln(t)ī+3tī − t²k, find the rate of change of f(x, y, z) along…

A: The answer is given in step 2

Q: Determine the radius of convergence of the following power series. Use the Ratio Test or the Root…

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Q: Consider the function Fx(x) = 0 x 2.

A: The given probability distribution is: 0x<0x20≤x<1k+1-kx-121≤x<21x≥2 It is known that FXx…

Q: The total revenue from the sale of x stereos is given by R(x) = 4,000 1 R'(x). OA. R'(x)=5.71- 4,000…

A: Given query is to find marginal average revenue.

Q: A boy owns 5 pairs of pants, 6 shirts, 5 ties, and 2 jackets. How many different outfit itom?

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Q: Evaluate the integral 36 S. 6 dx x( In x)4

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Q: lim X10 Select the correct choice below and, if necessary, fill in the answer box to complete your…

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Q: a. Find the first four nonzero terms of the Maclaurin series for the given function. b. Write. the…

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Q: Find the function with the given derivative whose graph passes through the point P. 3 g'(x) = 4 X +…

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Q: D. Determine whether each of the following series are absolutely convergent, conditionally…

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Q: Complete the table and use the result to find the indicated limit. If f(x)= O A. OB. O C. O D. √x+1…

A: The answer is given in step 2.

Q: Given f(x) = 2√. Which of the followings is the limit definition of the derivative f'(z). Select…

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Q: For what values of a, m, and b does the function f(x) satisfy the hypotheses of the mean value…

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Q: Find the area of the surface. The part of the plane z = 9 + 3x + 5y that lies above the rectangle…

A: Given  plane z =9 + 3x + 5y  lies above the rectangle [0,9] x [1,4]

Q: A triangle is bounded by the lines y = x, y = -x, and y = 1   When setting up an intergral to find…

A: Please see the below picture for detailed solution.

Q: 1 In 10 \ 10 dx X

A: Integral

Q: Find the most general antiderivative. [√t-√ dt

A: Recall the formula:∫tn=tn+1n+1+C

Q: Find the radius and convergence of the following: xn Σ (n!)2 n=1

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  substitute n+1…

Q: Use the properties of logarithms to write the following expression as a single logarithm: Int+7lnr –…

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