Two positive numbers have a sum of 87. What is the maximum product of one number times the square of the second number? Show your complete solution and box the final answer. write clearly and readable. Thank you.

Q: Problem 8 Find the following indefinite integrals: (a) [3r°dr (b) S(3r® +9x² – 12r)dr (c) S(7x-1…

A: topic- indefinite integral ∫xndx=xn+1n+1+C

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Q: Question 2 Determine the derivative of sec(x) tan(x) O sec z + sec z tan? x 2 sec? z tan x sec x O…

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Q: þr+2|dx -3

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A: answer is in next step

Q: If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)}…

A: If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)}…

Q: -3

A: topic- definite integral

Q: d f'(3).

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A: Here, let the given function be: f(x)=x2+ex-9⇒f'(x)=2x+ex Next,…

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Q: Solve the initial value problem. 4 y(x) = 4 sec(3.xr) tan(3x) ; y(7) = 3

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Q: Evaluate the following definite integrals. år 5.

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Q: sin a Determine the derivative of sec x sec x cos z-sin z sec tan e sec2 a O 1 1-sin x sec2 x sec2 x…

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Q: Find the area of the surface generated by revolving the curve about each given axis. *- 7t, y= st,…

A: Surface area genarated by revolving the curve about x-axis is parametric notion is…

Q: arcsin = ab' a? - Va? - y?; Find y!. Oy = 2abr(x+b) Va-y 1-y 2ab r Va- 1-y 2ab r/a-y H. 1-2ab z a- «…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x33 sin(x34) dx Submit…

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Q: 10 8. 10 If f (x) dr= 17 and/ f(x) dx= 12, then f(x) dr=5 A) True Ealce

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Q: A A A A A A A A A A AA A A A A A A A A A A A A A A A AAA 6. What is the sum of the series TC + ... +…

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Q: ェ-1 %3D the x-values at which f is not

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Q: 21 3x7 + 8x 5x

A: Given: y=3x7+8x5-215x

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A: Given problem:- Find the conservative vector field for the potential function by finding its…

Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: 10 8 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx =5. (A) True B) False

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Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: e8/n Σ 7 = 1

A: Given query is to find series converges or diverges.

Q: I have this math problem that I am very stuck on Suppose that a, b, and c are unknown constants such…

A: answer is in next step .please give a like.

Q: Vx² -9 What trigonometric substitution should be used to evaluate ? x2 A x=3 sece В x=3 tane C) None…

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Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: 4. a = 20 m [W 30°S] b = 30 m [W 40°N]. Find a - b. %3D %3D

A: We need to find a-b.

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Q: Find V· (V × F) if F(x, y, z) = 4 sin ci + 7 cos(9x – 10y)j + 10zk. V · (V × F) =

A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

Q: Calculus Use newtons method with the specified initial approximation x1 to find x3 the third…

A: Given

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A: Here, the given surface is  6x2+y2-3z2=4⇒f(x,y,z)=6x2+y2-3z2-4 Let, P(x0,y0,z0) be the point of…

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V × (V × F) =

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Q: If f(x) cos-(2x+5) 2, then dom(f) = %3D a+3 (A) (–3, –2) (B) [-3, –2] (С) (-3, —2] (D) (–1,1) (E)…

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Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: Use Newton's method with the specified initial approximation x, to find x3, the third approximation…

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Q: arcsin = ab x² – Va² – y²; Find y'.

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Q: 6. (ax3+ bx2+cx) dx= 2b | x2dx where a,b and c are constants. -9 A) True B False

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Q: Given a function f(x, y) = In(9 – x² – y²). (a) Find and sketch the domain of the function. (b) Find…

A: Given function f(x,y)=ln(9-x2-y2 )

Q: Let f(x) : Int dt. Find f'(x).

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 4 cos(t)i+5 sin(t)j+ 6tk;…

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Q: Describe the graph of the equation. r = 12 sin 6t i – 12 cos 6t j O Itis a circle of radius 6 in the…

A: To find: Discribe the graph of the equation

Q: tanode B В sec®

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Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. f(x) = cot x, a = - Po(x)…

A: As we know that; The Taylor series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at x=a.…

Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y? + z2 subject…

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Q: 422+3r-2 Given z+1 determine y" 18 (z+1) (z+1) 2 (z+1) 10 (z+1)

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