3. Graph and then find the area of the region bounded by the curves y = 8x - x² and y=2x−7.

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A: Given problem :- Consider the solid of revolution obtained by revolving about the x-axis the region…

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Q: 02:- a. b. Let u=x²-2xy + 2y³ with x = s² lnt and y = 2st³. Find ou/Os and du/ît. find the total…

A: In this question, we want to find the partial derivatives and total derivatives of the given…

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A:

Q: Given the equation z = arctan(x- y²) with the change of variables x=s³-t³ and y=st² + s²t, use the…

A: The objective of the question is determine the partial derivative of the given function at given…

Q: An ice cube is freezing in such a way that the side length s, in inches, is s(t)=t+6, where tis in…

A: Write down the equation of the volume.

Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: Solve for y at x=2: (4x^3 - 6yx^2 + 2xy^2)dx + (2yx^2 - 2x^3)dy = 0; y(1)=4

A:

Q: Write the following sets in set-builder notation. There may be more than one correct way to do it.…

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Q: Q5: Find the inverse Laplace transform of: f(s) = 3²(²-3)

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Q: h(t) = + 3²²-t t

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Q: x²-3 (x-1)² . Analyze and sketch the curve given by f(x)=- if y': 2(x-3) (x-1)³ 4(x-4) (x-1)* and…

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Q: Evaluate the following integrals. y = f(x) a. b. C. d. 16 0 f(x) dx [f(x) dx Ja (2|f(x) +3f(x) dx…

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Q: 3. f(x) = x-4 x+5

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Q: Suppose that a product currently sells for $24, with the price increasing at the rate of $5 per…

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 f(x) = Σ n…

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Q: Graph the function. f(x) = √√x+5 Plot four points on the graph of the function: the leftmost point…

A: Given problem:- f(x)=√x + 5

Q: 2|6x + 4 ≥ 1 OX - 7/12 O-7/12 - 12/7 choose the right answer

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Q: Question 12 If A is the area of a variable square with side s, what is the rate of change of A with…

A: Solution ) area of variable square A = s2  Differentiate with respect to s  dA/ds = 2s [ formula…

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A:

Q: (X^1/2 + 6) (X^3/2 -32)

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Q: x³dx S 17. √(1-x²

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Q: The graph of the function y = f(x) passes through the point (-1, 1) and the line tangent to the…

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Q: The equations x+y=6 and y=- -10-9 -8-7-6 -5 -4 -3 -2-10 -10 Determine the solution (s) to the system…

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Q: The graph below is the function f(x) 2 -5 -4 -3 -2 -1 2 B 4 -3 4 -5+1 Find lim x 2 Find lim 2 2 Find…

A: from graph limx→2- f(x) =-3

Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: 2. Differentiate. a)/(x)=12x¹ 5 -1 √√2-1 c) h(x)=- b) y = - 3x² 2x+3 - d) y = 21+1 31-2)

A:

Q: C- - 0 x4 (1-√x)5dx

A: we  need substitution method to evaluate given integral

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A: We need to find a.

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Q: 4. Let X: +3 if x < -2 if -2<x< 1 h(x) = {x² -x+2 if x2≥1 a) Find the following limits if they…

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Q: Find the general solution of the given ODE dy x + 2y - 3 2+y−3 = dx (x + y)² = C(x + y − 2) Option 1…

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Q: √-x if x1

A: Sketch the graph of f(x) Given information; The function is fx=-x,   x&lt;012x,      0≤x≤12x-x2,…

Q: Find the general solution for the following Second Order Deferential Equation: Q4: d²y dx² - y = ex…

A: Given: d2ydx2-y=ex+x2 So, we can also write as: D2-1y=ex+x2 The auxiliary equation of the…

Q: Find the general solution for the following Second Order Deferential Equation: d²y Q4: dx² - y = ex…

A: The given differential equation is;  d2y/dx2 -y=ex+x2.

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A:

Q: 7. Find the volume of the solid generated by revolving about the y axis the area between the first…

A: Concept: According to the shell method, the volume by revolution about the y axis is…

Q: Solve for y + In lyl at x=6: y'=(yx^2 - y)/(y+1); y(3) = -1 4.5

A:

Q: y=? € x ² y² + (y²) ² = 11 - U

A: see below the solution and calculation

Q: Use the Limit Definition of the Derivative to find f'(x) for the following function. You may NOT use…

A: Use limit definition to solve

Q: Use synthetic division to find the quotient and remainder when 2x3 -8x2 -1 is divided by x

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Q: mswer below: f(x) = f(x) = (x) = -2 68 5 4 3 2 10 1 0 1 -2 -3 -4 -5 6 -7 2 -00 4 6

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Q: How many odd three digit number can be written using the digits 2, 3, 4, 5, and 6?

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Q: Sorry, this

A:

Q: Which graph represents two functions that are decreasing on all points across the domain that is…

A: To find out the graph in which two functions are decreasing in the domain common to both.

Q: For vectors ?⃗ = ⟨2, −3, −2⟩, ? = ⟨1, −4, 2⟩ Find the projection of vector ?⃗ onto the vector ?.

A:

Q: If we try to apply Rolle's Thorem to the function f(x) = 2x² – 20x – 5 on the interval [0, 14],…

A: Here, the given function is: f(x)=2x2-20x-5 and the interval given is [0,14].

Q: √√√x if x1

A: Explanation of the answer is as follows