1/2 -1/2 4(8 + x)¹/² − x(8 + x)¯¹⁄² 8 + x

Q: The number of bacteria in a flask grows according to the differential equation dy/dt=0.09y In this…

A: The given data is: dydt=0.09y

Q: Consider the region R bounded by y=1-x² x = 0 and y=0 [This region is used to answer questions a -…

A: Given curve, y=(1-x2) and x=0 , y=0 The region R is by the curves,  y=(1-x2) , x=0 , y=0

Q: b. f(x+5)-1/2³+5

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Q: Match the differential equation with it's particular solution form. y'' + 7y' +10y = (4t + 5)e²t…

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Q: Consider the region between f(x) = x - 2 and the x-axis on [2,5]. For each line of rotation given in…

A: 38. The given data is: fx=x-2,  2,5 Around the line x=2

Q: Question: True or False: To evaluate the integral 1 | /9-² we use substitution with x = 3 tan 0,…

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Q: A particle moves according to the equation s(t) = 6 - , t > 0. Find its acceleration at time t.…

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Q: example г Find the centroid of the region bounded by the curves y = x ₁ x = 4 and the x-axis. (0,0)…

A: According to question,Given Curves,y =xx = 4andThe x-axis

Q: ex \e=-2) (e²+1) dx

A: To find integral

Q: B: Find Inverse Laplace Transformer for the following function:- 3s3-s²-3s + 2 45 F(s) = s² (S-1)²

A: According to question,Given function,Fs = 3s3-s2-3s+2s2s-12

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Using Trapezoidal rule

Q: The slope of the tangent line to the curve In (xy) = y² — 1 at the point (1, 1) is m =

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Q: the instruction is by using miscellaneous substitution. please edit the answer

A: Note:- Since you asked multiple solutions ,according to our policy we can solve first question for…

Q: Use the following function along with its first and second derivatives to do the following: A. Find…

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Q: 15. Evaluate the limit for the graph: lim f(x). *→2* 4 +∞o a. b. -1 14 A 2 -2 0 2 A C. d. 2 does not…

A: Solution:

Q: lim x-1 d x3+5 xa - X-5 * ха x2 + 4x -5

A: According to question,Given limit,limx→1 x3+5x2-x-5x2+4x-5

Q: -Calculate the minimum for the function f(x, y) = 2x² + 2x^² - xy

A: According to question,Given Function,fx,y = 2x4 + 2y4-xy

Q: Question: To evaluate the integral ve use | √2²-Adz, elect one: Substitution with x = 2 sec 0, where…

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Q: Determine whether the function f has a derivative at c. If it does, what is f'(c)? (If an answer…

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Q: Which of the following integrals are improper? (Select all that apply.) of 10x 1 7x - 1 dx 6 1…

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Q: S₁ 9 $₂ = 81 X $3 $4 55 9 Σ; 27-1 n = 1 = X

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Q: Evaluate the integral. 4 [ f(x -4 f(x) dx where 4 ) = {16-; f(x) = if -4 ≤ x ≤ 0 16x² if 0 < x≤ 4

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Q: Consider the function f(x) = xe 2, 0≤x≤ 2. This function has an absolute minimum value equal to:…

A: Given function is f(x)=xe-2x, 0≤x≤2 Differentiate f(x) with respect to x.…

Q: If f(x) = ax³ + bx² + cx+d, where a, b, c, and d are constants, find f"(x). 6ax+ 2b 6x + 2 a+b+c+d…

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Q: ke for this investment to reach a value of $11,800.00?

A: Given query is to find the investment to grow 11800.00

Q: Identify the vertex for: f(x) = x² +5x-2 O (-2,--5-) O (--/ -2) O (--/ -33) 33 O ( - 11/, --5-)

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Q: If f'(x) 0 for all x, which of the following could be a table of values for f? x -1 0 1 (A) f(x) 6…

A: If function f is decreasing then f’(x) &lt;0. Use this concept.

Q: By changing to polar coordinates, evaluate the integral L are tan (2) dy) dx. 0

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Q: Evaluate the limit lim 11e-3 using L'Hôpital's rule. After applying L'Hôpital's rule, the limit…

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Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

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Q: dw Use the Chain Rule to find &#: w = xysinz; Dx = xet, yet, zzaresin 2

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Q: Find the rectangular points.  (3,-120°)

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Q: Find the mass and the center of mass of the triangle with vertices (0, 0), (0, 3) and (2,0) assuming…

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Q: 1. Solve the following initial value problems: 1 y'=- with the initial condition: ty a) y (1)=2 b) y…

A: Since the student has mentioned to solve more than one questions but according to our guidelines,…

Q: 3x - 5 The total cost (in hundreds of dollars) to produce x units of perfume is C(x) = 9x + 2 (a)…

A: Solution is given below:

Q: √3 S 0 x√1+x² dx.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: particle moves according to a law of motion  s = f(t),   t ≥ 0,  where t is measured in seconds and…

A: Here we have to use application of differentiation.

Q: Investing: Inverse ETFs (Exchange Traded Funds) Inverse ETFs, sometimes referred to as "bear market"…

A: It is given that, The total amount invested in MYY, SH and REW is $10,000. Let the amount invested…

Q: Find ff xy + y dA, if D is the region: x² + y² ≤ 1, (x - 1)² + y² ≤ 1 using polar coordinates.

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Q: 2. Find the two x-intercepts of the function fand Show that f'(x)=0 at some paint between the two…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" + y = f(t), y(0) = 0,…

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Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Given: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing…

Q: 5.. Decompose the expression 1 (x² + 5)² (x−1) into partial fractions. Start by explicitly stating…

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Q: Problem #7: Evaluate the following limit. lim (x, y)→(0,0) If the limit does not exist then enter…

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Q: J. •[ 2 √ x² + 1 dx

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Q: The quadratic formula allows us to find solutions to any quadratic equation.

A: Give that, the quadratic formula allows us to find solutions to any quadratic equation. We have to…

Q: Question 2 Consider the following table of values: X 4 f(x) 3 4 2 1 f'(x) -5 -6 -7 11 3 g(x) 4 1 2…

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Q: You are standing above the point (2, 2) on the surface z = 15 - (3x² + 2y²). (a) In which direction…

A: Please see the below picture for detailed solution.

Q: Find the dimensions of the box with volume 2744 cm3 that has minimal surface area. (Let x, y, and z…

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Q: If f(t) = (t² + 6t+4) (2t² + 2), find f'(t). Find f'(3). Question Help: Video Message instructor…

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