2.2.7 Exercise Let X be a nonempty set and S the smallest o-algebra in X which contains all singletons {x}. Show that S = {A € P(X): either A or A° is countable}. نتا شبزر

Q: Find the derivative of sin In x O sin(Inx)/x cos(Inx)/x O cos(1/x) O sin (1/x)

A: topic - derivative of a function

Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. In n Σ n + ...

A: Given :∑ n=2∞ln nn+3

Q: 3. Find a fundamental matrix for the following system. Then find a solution satisfying the giving in...

A: solve the matrix

Q: A=1, D=0, U=0 ((A v D) · (D v U)

A: Here is the solution

Q: Determine the convergence or divergence of the series. (If you need to use co or -co, enter INFINITY...

A: This is sequence and series problem

Q: 2. A toy rocket is launched from a table 2 feet above the ground. The height of the rocket above the...

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

Q: A post 20 meters long stands vertically in a horizontal plane. Another post stands vertically on the...

A: Given: A post 20 meters long stands vertically in a horizontal plane. Another post 45 meters high st...

Q: Example 52. x log x dx.

A: ∫ xlogxdx ∫f(x)g(x)dx = f(x)∫ g(x)dx - ∫ (f'(x))∫ g(x)dx)dx   ∫ xlogxdx =∫ (logx)(x)dx              ...

Q: J. E n=1 Vn 2.

A: p-test series for a series to be convergence ∑n=1∞1np will diverge if p≤1              will converge...

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm2/min...

A: Given :radius of spherical ball is increasing at a rate of 2cm/minso, drdt=2cm/min

Q: 2π ||미 = 4, ||v|| = 16, 0 = 3 %3D %3D %3D

A:

Q: Match the sequence with the given nth term with its graph. 10n an n + 1 an an 10 10 8. 8. 4. 2 4 6 8...

A: here given  an = 10n/(n+1) for plotting put point 1,2,3,4...... first wwe put 1 a1= 10(1)/(1+1) = 5 ...

Q: What integration technique can be used to integrate: sec3 xdx Integration Formulas O Trigonometric S...

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Q: Find the solution of the differential equation that satisfies the given initial condition. dL dt = k...

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Q: Sg(x) dx 2. g(x) 3. 3f(x) dx 5. If(x)-g(x)] dx 6. [4f(x)– g(x)] dx

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Q: 1. The bases of a trapezoid are 22 and 12 respectively. The angles at the extremities of one base ar...

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Q: 1. Examine the given graph and evaluate the following. a) lim f(x) b) lim f(x) x→1+ c) lim f(x) x-1-...

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Q: (x – y)² = 2ax, find the y'if a is a constant x+y a. a-x-y a-x-y b. x+y x+y+a C. x-y x-y-a d. x-y

A: Differentiating the expression with respect to x

Q: Using the method of Lagrange multiplier, determine the minimum and maximum values of f(x,y,z)=2x+3y ...

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Q: Find the indefinite integral. X COS 9TX

A: Given,I=∫ xcos9πx2dxPut u=9πx2Differentiatedu=9π(2x)dxdu=18πxdxdu18π=xdxThereforeI=∫xcos9πx2dxI=∫cos...

Q: Find all the first order partial derivatives for the following function. fx, y, 2) - ze (ху) O af ze...

A: ∂ex∂x = ex.

Q: Find the radius of convergence and the interval of convergence. k(k + 1) k=1

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Q: Find dy/dx for: y= x2 cot x

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Q: Find the exact length of the curve. 23/2 12, 0 <x < 1 y =

A: Given : y=23x32,       0⩽x⩽1   To find : Curve length   

Q: In the quadratic equation Ax2+ Bx + C=0; describe the roots when 32 _ 4AC is positive. The roots are...

A:

Q: The functions represent the position of a particle traveling along a horizontal line, s(t) = 3t3 − 2...

A: for time t,t≥0 s(t)=3t3-20t2+48 t -20V(t) =dsdt =ddt(3t3-20t2+48 t -20)V(t) = 9 t2-40 t+48v(t)&gt;0 ...

Q: b. Si x-2ª 3 1

A: ∫13dxx-2    =  [ lnx-2 ]13   =  ln|3 - 2| - ln|1 - 2| =  ln |1| - ln |-1|   =  0 - 0  = 0 

Q: The integral of Cos x with respect to * A cos x +c B -sin x +c (c) sin x +c D) sec x +c

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Q: se separation of variables to find the general solution. (Use C for the constant of integration.)  ...

A:

Q: Solve the system of linear equations using direct method for an exact solution Cramcis x + 2x2 + 6x;...

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Q: Find u•v, where tetha is the angle between u and v llull=4, llvll=16, tetha=2pi/3

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Q: 2 XA)=T\(x+A) Coupunonz 12. Let f(x,y)3x2+y² find the relative extremum, and determine whether it is...

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Q: For the graph, calculate the following quantities.  1) y'(5) if y(x)=f(x)g(x) 2) y'(2) if y(x)=((f...

A: Given the graph 

Q: Graph of f 5. The graph of y = f(x) on the interval 0 < x < 5 is shown above. Which of the following...

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Q: V3, 3 2/3; + 8; i - k 4 1 83B k

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Q: Q3 Find domain and range for the following equations: 1) f(x) = 1- V, 2) f(x) = 3) f (x) = 4) f (x) ...

A: 1)f(x) = 1-xx is not defined for x&lt;0.Domain: [0, ∞)f(x) will have maximum value 1.Range: (-∞, 1)2...

Q: Find dy/dx for: y= (sec x)/x

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Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) + ...

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Q: Write the first five terms of the sequence with the given nth term. 6. 3 + - = 10 + - n2 %3D a2 %3D ...

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Q: A ladder 20 feet long is placed against a wall. The foot of the ladder begins to slide away from the...

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Q: 55. A cardboard box without a lid is to have a volume of 32,000 cm³. Find the dimensions that minimi...

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Q: Match the sequence with the given nth term with its graph. an = (-1)" an an 10 2- 8 1 ... 6. 4. 2 4 ...

A:

Q: Let R be the region inside the polar curve r = 2 sin 0 and outside the polar curve r = 3 – 2 sin 0 a...

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Q: 1 -1 -2 -2 -1 0 1 2 3 2 3 4 4 -2 -1 4. FIGURE 6.1.12. Spiral point (-2, 1) and saddle point (2,-1). ...

A:   Given the systemdxdt=2x-2y-4 anddydt=x+4y+3 To find critical point we take dxdt=0 anddydt=0  

Q: Solve using alternating series

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Q: A rocket is fired vertically upward from the ground. The distance s in feet that the rocket travels ...

A: Let s(t) denotes height  of a rocket at any time t. Then velocity of the rocket at any time t is giv...

Q: 4. Use the method of undetermined coefficients to find a particular solution to the system below. Pr...

A:

Q: Find the equation of the tangent line to y = arctan(2x) when x = V3 O y - = ( - ) 1 3 O y - = }(2 - ...

A: Let's find. 

Q: f (x) = 2x? – x +6

A:

Q: Find the derivative of the vector function below r(x ) = sin (secx 2)i +csc°(Vx² +1)j +8tan(x")k 1 A...

A: