5: Find the volume of the solid which is generated by rotating the region bounded by y=√x, y=x-2 and x-axis about: a. x-axis. b. y-axis.

Q: 13. Consider the functions f(x) and g(x) in the tables below. 5 6 7 8 f(x) 1 4 2 3 (A) g(x)= -f(x)+3…

A: topic- functions

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A: topic- arc length of a curve

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A: Given problem:- Define a polynomial function with all of the following properties. Roots: x=7, x=-8,…

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Q: Ive the given IVP using Laplace transforms. "-7x'- 8x = 0 x(0) = 1, x'(0) = -3

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Q: dx + 2x dx = 2x²y² dy

A: dx+2xdyy=2x2y2dy dxdy+2xy=2x2y21x2dxdy+2yx=2y2.......1equlet 1x=v differentiate with respect to y…

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Q: Find a formula for the inverse of the function. Select the correct answer. Or'(x)-(³²) ¹² 1/3 Of¹(x)…

A: Given problem :- fx=2-3x3 Find:- f-1x

Q: Question 20 (5 points) Find the limit. 00 ∞ 5 0 -15 Question 21 (5 points) Find the limit. 0 1 00…

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Q: 3. Find the average rate of change of function f(x) = 4 - 2x² (a) On [0, 1] (b) On [a, a+h].…

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Q: Represent the plane curve by a vector-valued function y=1-x^2

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Q: Find the arc length of the graph of the function over the given interval. y = In x, [1, 8]

A: We have to solve given Questions.

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Q: Evaluate lim (x) x-0 f(x) . . . . . . . . . . . F . . y 4 f(x) g(x) X

A: See this solution in below

Q: Suppose the position function of a particle is given by r(t)=(√3 sin(t), t-2, √3 cos(t)). If the…

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A: We have to choose correct option.

Q: Consider the graph of f'(x) given below. At what value(s) of x does f(x) have a local minimum? If…

A: we have given the graph of f(x) we know that at maxima and minima f'(x) =0  (means slope at that…

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Q: 9. If = 1, 4, 5) and W = (2, -3, 1 V ( − w a) 3-2W b) |v|

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Q: Find the Taylor series centered at c = -1. 7 3x-2 f(x) = Identify the correct expansion. ∞ 3" - 7 Σ…

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A: I am attaching image so that you understand each and every step.

Q: It f(x) = x² - 4x - 3, find f (x + 3). 10. If g(x) = 2x³ + 4x − 5, find g(x − m)

A: 9) The given function is: f(x)=x2-4x-3

Q: Find the curl of the vector field F curl F = (2y cos(x), 5x sin(y))

A: F = (2ycosx , 5xsiny) find curl F =?   curl F  = dF2/dx - dF1/dy here  F1 = 2ycosx  F2 = 5xsiny now…

Q: 12. For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet,…

A: Topic = Integration

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Q: [tanh (0.12 – j0.05) ]In(sinj0.5)

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Q: According to the ideal gas law, the pressure P, temperature T, and volume V of a confined gas are…

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Q: Part 2. Integration by substitution Solve the following integrals through video presentation. √x+1 x…

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Q: Step 3 Rewrite the integration in terms of u and v. 110 Step 4 (cos w)ew dw = (cos w)ew - Again…

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Q: The one-to-one function fis defined below. 3 f(x)=√√/2-x+7 ¹(x), where f¹ is the inverse of f. 1…

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Q: (6xy - 3y² + 2y)dx + 2(x − y)dy = 0; when x = 0, y = 2

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Q: Solve the initial value problem y" + 10y' + 25y = 0, y(-1) = 5, y'(-1) = 3. y(t) =

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Q: How much must be deposited today into the following account in order to have $65,000 in 5 years for…

A: Given :Future value =F=$65000Present value =P=?Rate = r=6%=0.06Time=t=5 years

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Q: Approximate the area under the curve graphed below from x = 2 to x 6 using a Left Endpoint…

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Q: Problem 1 Find a linear differential equation with constant coefficients satisfied by e²x, e*, e³x,…

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Q: Use the derivative f'(x) = x²(x - 5)(x + 5) to determine the local maxima and minima of f and the…

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Q: Find the critical points of the given function. 5. f(x) = 2/3+2/3 +x-2/3 6. f(x) Va 7. f(x) (3x +…

A: Given: 5)     fx=14x43+x13+x-23 After simplifying we get     fx=14x43+x13+1x23 Critical points:…

Q: cos-¹ Q6A)If y cos = prove Zyy + z = 0. B) Z = (1 + i)(2-1)-¹, find |21. 倉

A: Simplify given equation in z then  two times partially differentiate z

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A: Given :- u =(3,2) , w=(2,-1),v=(-6,-4)  Write v as linear combination of u and w

Q: Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which the normal line…

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Q: Consider the differential equation x²y" + xy + y = 0; cos(In(x)), sin(In(x)), (0, ∞). Verify that…

A: Solve couchy Euler differential equation by putting y=x^m