Find the largest product the positive numbers x, y, and z can have if x² + y + z = 4. The product is (Type an exact answer, using radicals as needed.)

Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

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Q: 10. Determine the point on the line x + 2y = 2 that is closest to (0, 0). Draw a sketch.

A: point which is closest to origin

Q: Find f'(0) if f(x) = a; a, b, c, d constant bc-ad O d² ad-bc (c+d)² ad-bc d² ad+bc d²

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y=x²-In(x),…

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Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

A: We have to choose correct option for given questions.

Q: Since the creation of a social program, the percent of persons 65 years and over with a family…

A: Here we have to us ethe given function.

Q: B)Convert r = √2 cos (0-) to cartesian.

A: we need to convert polar coordinate into cartesian.

Q: let a a E R - {0} and g the function defined by : sen (2) si z #0 az g(x) = 5 si z = 0 The function…

A: In this question, we want to know for what value of a , the given function g will be continuous on…

Q: Find the slope of the tangent line to the graph of the given function at the given value of x. 1/2…

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Q: Suppose that the total profit function for a company is given by P(x) = 4x³ — 210x² + 3600x - 200,…

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Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

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Q: Find an equation of the tangent line to the graph of y = x³ – 3x – 1 at the point (2, 1). 09x - 2y -…

A: 1.y=x3-3x-1 at the point (2,1)2.y=logx2e

Q: What are all the values of k for which f* x² dx = 0? 3 -3 and 3 0

A:

Q: B)Solve differential equation dy -(x²+y) = dx x+siny

A: Given that,

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

A:

Q: A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles…

A:

Q: Find , given y = 5² 6n² a dy dx

A: ddx(5x6ln2(x))We know that…

Q: Evaluate x³ 2x² +7 dx S x² Ox² - 2x - 72 +0 0²-2x - 1 + C X O2+2 +c+C -2+7ln x² + C -

A:

Q: B)Prove (cose + i sine)" = cosne + i sin no

A: Solution is given below:

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: We need to find area.

Q: 6. 7. 3+6s+45²-25³ s² (s² + 3) 26-5²- s(s² + 4s+13) [2+1+√√3 sin √√3t-4 cos √√3t] 2 [2-3e-2t cos 3t…

A: To find the inverse laplace of the following.6 3+6s+4s2-2s3s2s2+37 26-s2ss2+4s+13

Q: Q5A) Find volume of body from above Z = √√4-x² - y² and below Z Triple integration. 1 using

A:

Q: 13. Find the distance from the point (2, 2, 3) to the plane 2x+y + 2z = 4.

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Q: Evaluate f(sinxcosx + tanxsec² x) dx O-[sin²x + tan² x] + C O tan²x - sin²x + C O sin²x - tan²x + C…

A:

Q: 11.Sketch the graph of the region D and evaluate the double integral y dA, D = {(x,y)| 0≤ x ≤ ¹,0 ≤…

A: The region D is bounded by the below curves:x=0 to x=1; y=0 to y=x3.

Q: Solve for m ffm m(8xy + x?)dxdy =3, 0<y<x<1

A: we can solve as follows

Q: (2) Find an expression for the area under the graph of f as a limit. Do NOT evaluate the limit. g(x)…

A: given :   g(x)=x+lnx

Q: Solve using Inverse Operaators. y"" - y = 4e-x + 3e2x; Particular Solution: Y=C1+ C₂ eax + C3 ebx…

A: Given that,

Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: Given

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4…

A:

Q: 3 X and f'(-2) if f(x) = 6x. 8 (-2)=(Simplify your answer. Type

A: Given: f(x)=x38-6xTo find:f'(-2)

Q: Find the general solution of the differential equation y" 10y +34y = 0. NOTE: Use cy and ca as…

A:

Q: Consider the following sequence x₁ = √₁, x₂ = √1 + √I, x3 = √1+√₁+√₁ Evaluate lim xn (No credit for…

A: The given sequence,x1=1, x2=1+1, x3=1+1+1

Q: You need a 50% alcohol solution. On hand, you have a 110 mL of a 10% alcohol mixture. You also have…

A:

Q: ( (tano-1)² do

A: Given ∫[tanθ-1]2 dθTo evaluate the integral:

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A:

Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

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Q: Evaluate f(2x² + 3x + 1)5 (8x + 6) dx

A:

Q: Q2A)Matrix 4 = [],find Eigen values of 4². A

A: The given matrix is  A= 1342. We have to find eigenvalues of A2. Eigenvalues are the roots of the…

Q: -)Find volume of body from above Z=√√4x² - y² and below Z Triple integration. 1 using

A:

Q: Given the following limit, select all statements that must be true. lim h→0 Select all that apply:…

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Q: The first thing “e” wanted to do is to “Calculuize” his favourite game, apples to apples. So, one…

A: A box for the apples to apples game such that its width is exactly three times its length and its…

Q: Given : y = cot √2x + 1 Find dy dx O csc² √2x + 1 √2x+1 O csc² √2x + 1 2√2x+1

A:

Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: We need to determine Maclaurin series for xarctan(x2).

Q: The plot below represents the function f(x) 8+ 7 4 5 6 5 4 3 2 1 -5 -4 -3 -2 -1 -1 1-24 Evaluate…

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Q: The position in feet of a race car along a straight track after t seconds is given by s(t) = 4t² - t…

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Q: Let f: A→B be a function, and X⊆A.Prove or disprove: f(f^−1(f(X)))=f(X).

A: Let f: A→B be a function, and X⊆A.Prove or disprove: f(f^−1(f(X)))=f(X)

Q: (a) (8,4) r> 0 r 0 r 0 r< 0 -5) 3 = = (r, 0) (r, 0) = (r, 0) = (r, 0) =

A: Follow the procedure given below.

Q: 1 1² +49 When solving O a) I = [sen (0) de Ob) I=tan(0)de O c) I = cos(0)de I= O d) I-sec(0)de I=…

A:

Q: 1. Find each of the following derivatives. d a. dx (4 sinx) b. [ln (2x4 - 3x)]

A: We have to find derivative of given function.