Q1) Determine if the following integrals converge or diverge. If the integral converges determine its value. dz 2² - 9

Q: 11. Rules of Definite Integrals: If f(x)dx =12, S" S(x)dx = 6, and "S(x)dx= 4 , find the following:…

A: We need to perform integral.

Q: Find the Maclaurin series for the given function f(x) = e-6x

A: The maclaurin series is: f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x…

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Q: Use the integral test to determine whether the series converges. Σ 4n - 1 n=1 converges diverges

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Q: Find Σ +i . Ο 30 Ο 31 Ο 32

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Q: 12 For the given function y 3 cos ( 0 2 state the following (show al Work) a) Amplitude b) Period c)…

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Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Remember that we are looking for the value of the initial velocity, v(0), if the maximum height is…

A: topic- equations

Q: Use an appropriate test to determine whether the following series converges. 7 Σ 3 k =1 VK

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Q: S(e3t + e-3t)2 dt

A: To evaluate the value of given integral.

Q: Find (3+2) - 2i . 406 754 386

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Q: 1 Find the Fourier series for 1, if -п <х <0 { { -1, f (x) = -1, if 0 < x< n

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Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: 2x 3x Evaluate the given limit of lim + if it exists. I – 1 I +1

A: Follow the procedure given below.

Q: S 2x(ex²+1 – 2x*) dx

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Q: Would it be more difficult to find the points where there is a horizontal tangent line to this…

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Q: QUESTION 3 Find a formula for the nth term of the sequence. 1, 4 9' 16 25 (reciprocals of squares…

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Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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A: Given problem:-

Q: Find the Maclaurin series for the given function f(x) = e-6x

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Q: 1. Consider the function f(x) =-2(3x– 3)* + 1. a) State transformations. b) Use TWO of the following…

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Q: Determine the explicit formula for the nth term of the sequence written below. Note that the first…

A: To determine the explicit formula for the nth term of the sequence written below.14, 13, 25, 49,…

Q: (425 + 62?)dx Find -2

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Q: Use right and left endpoints and the given number of rectangles to find bwo approximations of the…

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Q: Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 convergent or divergent. b)…

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Q: Complete the equation. x- 7 arctan arccos %3D 7. 7 < x < 14

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Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: We need to solve differentiation problem.

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

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Q: Find the differentlal dy of the glven function. (Use "dx" for dx.) y = BVx + dy =

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Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…

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Q: cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

A: Given query is to find the rate of change of distance between the cars.

Q: Solve the following problems. 2. 2x°cos 5y+ x tan5y dy=0

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Q: S2 2 sin?x cos5x dx =?

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Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: ng Part I of the Fundamental Theorem of Calculus, evaluate: da t'dt =

A: Given query is to find the derivative of the expression.

Q: Find the area bounded by y = x + 4 and y = x² - 2. Answer:

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Q: Consider the series E (-1)"(3x+6)" . Find the series radius and interval of convergence, n=0

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Q: Express the series using sigma notation. -6m – 3m + 0 + 3m + 6m ...

A: Given -6m-3m+0+3m+6m...

Q: Glven fx) dx = 9 and fx) dx = -4, evaluate the following. Exercise (a) Step 1 To evaluate the…

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Q: Find the limit of s(n) as n . 1 n(n + 1) s(n) = 5.

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Q: An advertising agency spends £x on a newspaper campaign and a further £y promoting its client's…

A: The Multiplier Method of Lagrange We may need to maximize (minimize) a function that is constrained…

Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…

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Q: 5) Find cos (20) if tan @) =Ž and e is in quadrant 3.

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Q: Consider the function f(x) = 2x – 6x² – 48x + 1 on the interval [– 6, 8]. Find the average or mean…

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Q: Szax -x2 EVALUATE THE FOLLOWING 1. cot x dx 4 sınx + cSC X 2. X sınx cosx dx S2) dx S cec'y dy 5. In…

A: We have to solve above integral

Q: Identify the given differential equation as to the dependent variable, degree of equation, whether…

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Q: C. Find the general solution of the given variable separable equation. 1. 2cosx cosy dx - 3Isin x…

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Q: Find E( +1)? O 367 418 O 423

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Q: Find f' (x), if f (x) = 3Vx + 2Vx – 11 %3D

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Q: Evaluate the Integral using the following values. 8. * dx = 1,020, x dx = 30, dx = 6 (7x 11x +4) dx…

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