When calculing the Laplace transform of the function f(t)=t-sinh(t) is obtained as a result: A- F(s) = F(s) = -2s s² - 1 2s (s² - 1)²

Q: Find the maxima and minima of the function f(x, y, z) = xy²z³ under the condi- tions x + y + z = 6,…

A: The given function Let

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Q: 16) Use Newton's method to approximate the indicated solution of the equation correct to six decimal…

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Q: Find the area of the shaded region. square units 2 + 1 -1 -²4 2 +3 y=x-2 3 4 y=√x

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Q: An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out…

A: An open top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out…

Q: If f is decreasing and f(x) > 0 on an interval, I, then g(x)= 1 / f(x) is increasing on I. True O…

A: Given that, If is decreasing and  on an interval , then  is increasing on .The aim is to determine…

Q: The graph of the function f is shown. 4 2 0 -2 -4 -6 -8 -10 O-6 only For what values of c does lim…

A: the graph of f(x)

Q: Find af Әх af ду af дz af af Әх ду af = ду = and f(x, y, z) = Find their values at (0, -1, 1) if…

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Q: Let F(x, y) = x³ + y³ − 3x − 12y + 20. Find the critical points of H and classify the kind of local…

A: The given function is .

Q: Let S be the solid that lies between the paraboloid z = x² + y² and the sphere x² + y² +z² = 2. (a)…

A: Given that  S is the solid that lies between the paraboloid and the sphere The graph of solid

Q: Let f(x): = 10 - 2x. (a) Sketch the region R under the graph of f on the interval [0, 5]. y 10 8 6…

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Q: For which value(s) of x does f (x) = 2x³ – ¹9x² + 19x + 2 have a tangent line of slope 5? If there…

A: The given function is

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 4t, where 0 ≤ t ≤ 2.5…

A:

Q: Write an equation for the ellipse. Type the left side of the equation in the box below. =1 *** COB 2…

A: The standard equation of an ellipse with a major axis parallel to the x axis and center  is

Q: Find all vectors u that satisfy the equation (1,1,1) xu= (-6,1,5). Select the correct choice below…

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Q: 5. 0 sin x 1-x² dx

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Q: The polynomial C(t) = -0.006t4 +0.140t³ -0.53t² +1.79t measures the concentration of a dye in the…

A: C(t)=−0.006t4+0.140t3−0.53t2+1.79t

Q: Evaluate π [15. 0 T $15 0 15. 1 - cos x 2 1 - cos x 2 dx = dx.

A:

Q: If the marginal revenue (in dollars per unit) for a month is given by MR = -0.3x + 400, what is the…

A: If the marginal revenue (in dollars per unit) for a month is given by To find the total revenue from…

Q: Using the sum and difference of cosines formula, find the exact value of cos Enclose numerators and…

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Q: Find the indefinite integral. 20eSt /√30 √5 + est dt Do not include the constant "+C" or any…

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Q: 2η 3. Σ. 1 n=1 nn

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Q: In preparation for the NEXT problem, find the derivative of the SINGLE VARIABLE function. h(x) =…

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Q: Find the Taylor series for f(x) = ln(x) about a=2. Find the interval of convergence.

A: Taylor series of ln⁡(x) around a=2A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: A particle moves along a straight line with equation of motion s = f(t), where s is measured in…

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Q: Determine the resulting definite integral after making the following substitution: Se dx where u=lnx…

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Q: A student council consists of 15 students. (a) How many ways can a committee of eight be selected…

A: Given that total number of students = 15a) number of ways to select a committee of eight= b) Let A…

Q: x=2(y-2)³/2 from (0, 2) to (2, 3)

A: 3.x=2(y−2)3/2 from (0,2) to (2,3)x=2(y−2)3/2Using the power Ruleddxxn=nxn−1

Q: Use Stokes's Theorem to evaluate b F dr. In this case, C is oriented counterclockwise as viewed from…

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Q: Question The graph of f(x) is shown below. Find the graph of f'(x). VA -6-5-4-3-2-1, 1 2 3 4 5 6 MN

A: A graph of the function  is given.The aim is to sketch the graph of the derivative function .

Q: 3. Is there a relation between the domain of a function and its interval of convergence?

A: From the given statement

Q: 1 Estimate the area under the graph of f(x) x + 2 rectangles. Round your answers to four decimal…

A: The given equation of the function  over the interval

Q: 1. Write the binomial expansion of the expression: (2x² − y)³

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Q: The figure shows the areas of regions bounded by the graph of f and the x-axis. f d f ( x ) d x…

A: Using the definite integral property∫acf(x)dx=∫abf(x)dx+∫bcf(x)dx

Q: The total profit from selling x units of cookbooks is P(x) = (2x-2)(4x-9). Find the marginal average…

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Q: Determine the resulting definite integral after making the following substitution: • ¹/3 So 1 4+9x²…

A: I =∫01/314+9x2 dx

Q: Suppose k(x) = f(g(h(x))). Given the table of values below, determine k'(-2). f(x) g(x) h(x) f'(x)…

A: xf(x)g(x)h(x)f′(x)g′(x)h′(x)−2−4−1046−7062−11−3820−5−8237

Q: The total revenue from the sale of x stereos is given by R(x)= 3,000| 1- sale of x stereos, R(x). O…

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Q: Select the graph for which a) ƒ¹(x) > 0 and f11(x) > 0

A: It is given that, the f'(x)>0 Which means the function f(x) is increasing.Therefore Graph-a is…

Q: Express the vector P₁ P₂ in the form v=v₁l+V₂j+V3k if P, is the point (0,5,0) and P₂ is the point…

A: given  and

Q: -6-5 +3 3-2-1 I LE 2 LUI 45 HH 1 2 3 4 5 6

A: We know that for any given function f(x)f′(x)>0 where f(x) increases

Q: For Questions 1 and 2, region R is bounded by f(y) = y²- 14 and g (y) = 2y +1. Which of the…

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Q: A Norman window is constructed by adjoining a semicircle to the top of a rectangular window, What is…

A: In the Norman window, the length and breadth of the rectangle is . Also the diameter of the…

Q: Let F(x) = * sin(7t²) dt. " Find the MacLaurin polynomial of degree 7 for F(x). Use this polynomial…

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Q: Below is the graph of f(x) = 5x³ - 4 and the line y = 3x + 7. Graph a line tangent to the graph of f…

A: The given equation of function is  and equation of line

Q: 17-22. Position from velocity Consider an object moving along a line with the given velocity v and…

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Q: Locate and classify the extreme points of the function f(x, y) = 8x³ + 6xy + y³.

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Q: a) Find a potential function for the vector field, i.e., find a function ƒ so that F =Vƒ. b) Use the…

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Q: a) dx dy b) = dx c) = ln(x) ex dy dx = x² + e¹0x = yx³ if y(0) = 4 ifdy |x=1 = e² dx if y(0) = 1

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Q: The region bounded by y=x^2−3x+2 and y=0 is rotated about the y-axis. Find the volume of the…

A: Region is bounded by y=x2−3x+2 and y=0Rotating the region about…