Find the arc length L of the graph of r(t). r(t) = 4 cos(t)i + 4 sin(t)j+ tk, 0

Q: ¤(x+4)~²dx

A: Here we have to find the given indefinite integrals.

Q: Q4 Find the eigenvalues and eigenvectors of the matrix: 21 1 -1 2 -2 1-1

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Q: 4- Find lim,: ( -) 10 20 (You cannot use numerical table method). tan(2)-1 tan?(2)–1)

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Q: Consider the following functions. f(x) = 6x – 5, g(x) = !! 3. Find (Fo g)(x). Find the domain of (Fo…

A: f(x)=6x-5  , g(x)=x3Consider(f∘g)(x)=f(g(x))             =f(x3)             =6x3-5…

Q: Graph the feasible region. x + y 2 3 -x + y 2 1

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Q: dy 5. -2ty + 4e-t² dt y(0) = 3

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Q: Find the solution of the following IVP using Laplace transforms given that f(0)=1 and f (0)=2: d…

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Q: Solve for the function that will satisfy the given Bernoulli Differential equations: dy/dx + (1/x)y…

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Q: 13. Explain in your own words what a limit is. Use several diagrams and be sure to consider lim…

A: This is a problem of limit. Based on the general formula we will answer the question.

Q: Find the cost function for the given marginal cost and fixed cost. See Example 8. Marginal Cost…

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Q: Given the differential equation y'' – 5y' + 3y = – 4 sin(5t), y(0) = – 2, y'(0) = 1 | Apply the…

A: Given,  y"-5y'+3y=-4 sin(5t)

Q: Consider the region bounded by x = 3y and x = y^3. A solid is formed by rotating the region about…

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Q: 2x3 + 1 x3

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Q: dy Suppose 9 x²– 2 ( 3 x³-2x+3) and y(1) = 3. dx What is y(2)?

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Q: Recall that csc(x) and cot(x) = sin(x) cos(x) sin(x) d4 cot(x) The ratio dx csc² (x) is a constant…

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Q: Find the interval of convergence for the given power series. (* – 11)" n( – 10)" The series is…

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Q: The function f(x) = – 4x* + 6.24x² + 53.784x + 1.62 is increasing on the open interval ( It is…

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Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: Find the expression of the general term of the sequence given by 3 5 7 9 11 1, 2'6' 24' 120 ' 720 2n…

A: The given sequence,      1,32,56,724,9120,11720

Q: Find the particular solution of the following ODE given that y(0)=7 and y'(0)=0: d’y dy dx -+3-10y=0…

A: To find the particular solution of ode

Q: nd the linearization of f(x)= {Vx at c = 64. Use the linearization to approximate 64.05.

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Q: Find the exponential function y = Cekt that passes through the two given points. y = y (0, 7) 6- 5 4…

A: Given query is to find the function.

Q: Let f(x) = 6 + v4x – 5. Find f-'(x). f-(2) = for x > 6

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Q: 2/ Find the value of the limit: lim x/*,

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Q: Use Newton's method to approximate a root of the equation x + x + 4 = 0 as follows. Let 1 = - 1 be…

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Q: Use Newton's method to approximate a root of the equation +x + 4 =0 as follows. Let 1 = - 1 be the…

A: The given equation,    x3+x+4=0

Q: Find the arc length L of the graph of r(t). r(1) – ittj Vor? k. 1 r(t) = t i+tj 2 <t< 5 L = i

A: To find the arc length L  of the graph of r(t).

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) (t) = (e-e 2 %3D L{f{t)}…

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Q: dy = 2 x cos ( 3x² ) and y(0) = 1. Suppose d x What is y(1)?

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Q: A bacteria culture is growing at a rate of r(t) = 8e0.6t thousand bacteria per hour after t hours.…

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Q: 2. (6x-2) dy d2

A: Given query is to find the value of the integral.

Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(x)

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Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: For 3 random distinct positive real numbers: • the sum of the two smaller numbers is 12 less than…

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Q: Evaluate the integral. HINT: [Use a shortcut.] e 8x - 1 dx

A: Using substitution ,

Q: Consider the function f(x) = -4xi + V24 -x on the interval [7, 27]. Find the absolute extrema for…

A: We want to find absolute maximum and minimum.

Q: Suppose that f is a continuous function such that = -12. Find xp (r)f P(*") dz.

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Q: A rotating light is located 15 feet from a wall. The light completes one rotation every 5 seconds.…

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Q: The difference between f'(3) and f'(x) is that f'(3) is a numerical value and f'(x) is a function of…

A: Explanation of the answer is as follows

Q: 2. Find the area bounded by a curve x = y - 2y? - 3y and the x- axis 3. Find the area bounded by a…

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Q: dy Suppose 2e-2r and y(1) = 4. dx What is y(2)? O 3.117 O 3.567 O 4.117 O 4.135

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Q: he acceleration function (in m/s²) and the initial velocity v(0) are given for a particle moving…

A: Given query is to find the velocity function and the distance traveled.

Q: The function f(x) : 2x3 – 27x? + 84x + 8 has one local minimum and one loca This function has a…

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Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

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Q: 3. Consider the graph of y = ln (x) + 1. Calculate the area enclosed by the curve y= ln (x) +1 and…

A: The region is bounded by y=ln(x)+1 and the y-axis between the lines y=1 and y=2

Q: Evaluate the indefinite integral. Sa V1 – x? daæ - cos° 0 – cos' 0 +C } (1 – a²)%/2 – }(1 – 2²)/² +…

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Q: Differentiate the following functions: i. v = 15/7(12/7+ 3t) (2x – 9) f(x) = x + 4 ii. iii. y =…

A: We can solve this as follows:

Q: is said to be the Laplace transform of f, provided that the integral converges. to find L{f(t)}.…

A: Let's find.