Find the area of the region between the curves: y = √√√x and y = x² from x = = 0 to x = 2

Q: dy Write down a differential equation of the form =ay + b whose dt 7 solutions all approach y = = as…

A: We have to write down a diffrential equation of the form  whose solutions all approach  as

Q: Let F(x, y, z) = z tan−¹(y²)i + z³ In(x² +9)j + zk. Find the flux of F across S, the part of the…

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Q: Using the u-substitution, u = x + 2, identify f such that the integral [TVT [ f(u) x + 2 dx, takes…

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Q: Solve the Initial value problem zy(x) y"+14y'+50y = 0, y(0) = 2, y'(0) = −17

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Q: why is the derivative of (sin(bx)ln(a)) = (ln(a)cos(bx)b)? why is ln(a) treated as a constant?

A: We have the following expression:sin⁡(bx)ln⁡(a)Here x is the variable and a,b are constants

Q: a. Sketch the graph of a function that satisfies all of the given conditions. Note that you need to…

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Q: Find domain and range f(x)=x^2-5x+6/x-2

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Q: Find an equation of the tangent line to the curve at the given point. y = 3x³ x² + 2, (1,4) y =

A: Using application of derivatives, we can find slope of tangent and thus it's equation.

Q: 2-54. Consider a home you purchase for $600, 000, at a down payment of 15% and at a rate of 4.5%.…

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Q: 7. Find the absolute maximum and absolute minimum values of fon the given interval. a. f(x) =…

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Q: Answer the following questions for the function f(x)=x√√√x² + 1 defined on the interval -7 ≤ x ≤ 4.…

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Q: 19-26. Evaluating limits graphically Sketch a graph of f and use it to make a conjecture about the…

A: We say that the limit of a function f(x) exists at a point x=a if the value of f(x) approaches same…

Q: 1 Decide whether the sequence an converges and if so, calculate limno An : 3n - 2n 4n an

A: To decide whether the sequence  converges and if so, to calculate .

Q: Use the graph of F, shown on the right, to find the given limit. When necessary, state that the…

A: We want to calculate a limit involving a variable x approaching to the right of a certain value…

Q: If lnx = 700, find x.

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Q: 2) Let g(x, y) = x³ − 6x² − y + 5. Find and classify the critical point(s) of g.

A: g(x,y)=x3−6x2−y+5

Q: Use undetermined coefficients to find the particular solution to y"-2y-15y = 2e-3t Y(t) =

A: The given differential equation is

Q: (n75)”. What is the limit of $₁,? (C) e (D) 0 Let (sn) where sn = (A) The limit does not exist (B)…

A: given that

Q: Use the n-term test to show the following series is divergent. Σsin n=1 n² +1

A: By using the nth-term test to show that the following series is divergent.

Q: Q65 8t Applying the shifting property to ascertain the Laplace transform of est cash (at)…

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Q: T 1 m Į 1-1/² -y=1 -2 m x

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Q: Calculate the integral approximations T4 and M4 for -2 (In x)-² dx. Your answers must be accurate to…

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Q: 1) Find the derivatives of the following functions: a) x³e b) sin(x³ + 2x) I c) 1+x²

A: We are authorized to answer three parts at a time, so we are answering the first three parts. Please…

Q: Suppose that the function fis defined for all real numbers as follows. f(x)= 1-x²_if_ x<1 -2x-3 if…

A: we have given a function

Q: Calculate the integral approximation Sg for 6 √₂ 72²1 dx. S8 =

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Q: 5. Find the equation of the line that passes though the point (-2,4) and perpendicular to 3y - 9 =…

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Q: Is it possible to find an integer n such that fo and is convergent? If it is possible, you must show…

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Q: C. Simplify after removing all symbols in grouping 3x-[(7y-5(8x-2y+32)-11x)-6y-z] 16.

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

Q: 11² F = (eª sin y, eª cos y, yz²) S is the surface of the box bounded by the planes x = 1, y = 2, z…

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Q: 5. Explain how you would use the limit comparison test to determine if the following series is…

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Q: Residents of the town of Maple Grove who are connected to the municipal water supply are billed a…

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Q: Verify that the following functions u is harmonic, and find a conjugate harmonic function v. u(x, y)…

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Q: Compute the indefinite integral dx 16 + 9x2 S || sin (a) 8x dx 16+ 9x2 8 45

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Q: Compute the indefinite integral S dx 8x4 Remember that you must wrap any functions such as sin (x)…

A: The given integral is .The aim is to solve this integral.

Q: Find the indefinite integral. Include a multiplication sign between functions. For example, z. e². |…

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Q: .Jeremy bought x pounds of peanuts for $4.50 per pound and y pounds of cashews for $7.05 per pound…

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Q: Let F =< xe, xe, zey Use Stokes' Theorem to evaluate where [[ curlF J curlF.dS, S is the hemisphere…

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Q: 6 S₂ 7²1 dx. 2 S8 = 3 FI

A: Using simpson rule, we can estimate the given integral.

Q: 6 5 4 3 2 y 0 1 ¦ y = f(x) 1 2 3 5 6 7 8 9 Enter each answer as a whole number (like -4, 0, or 253)…

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Q: (d) What is the maximum value of f? The maximum value is (e) What is the minimum value of f? The…

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Q: What hap f(n

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Q: Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional…

A: According to the given information water leak rate is proportional to the square root of the volume…

Q: Compute the indefinite integral dt t(36+In² t) S Remember that you must wrap any functions such as…

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Q: The graph of a rational function fis shown below. Assume that all asymptotes and intercepts are…

A: The given graph

Q: Find the indefinite integral 6x² sin(5x)dx. 6x² sin(5x) dx integral 6a [62 help (formulas) Use a…

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Q: Use the given pair of vectors u = u+v= uiv= 2u - 3v = (4,2), v = (-2,-1) to compute

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Q: Find and simplify each of the following for f(x) = 8x-9. (A) f(x + h) (B) f(x+h)-f(x) f(x+h)-f(x)…

A: f(x)=8x-9

Q: how do you evaluate the following integral without dividing it into two parts? ∫(0 to ∞)  ​x−2dx

A: To evaluate the following integral.

Q: A thermometer is taken from a room where the temperature is 21°C to the outdoors, where the…

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Q: Evaluate the following limits (a) limx→+4-4 t-9 (b) limn→9 √√t-3 x²-16 √x+4-1 (c) limx→-3 x+3

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