Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an} is convergent and find its limit. = 3 an+1 -

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A: To find out the curl of the given vector.

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A: Given: function f(x)=-1+x1-xwe know that11-x=1+x+x2+x3+..........=∑xn0∞where…

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A: Topic = Derivative

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. 9 3 cos 0+2…

A: Let's convert to Cartesian equation.

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

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A: Concept: Linear approximation: The definition of a linear approximation of a function is simply…

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Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: The given nth term is: an=27n+7 Determine the convergence or divergence of the sequence with the…

Q: f(x) =  4x x − 2 where h ≠ 0 f(a + h) − f(a) h  =????

A:

Q: لما D the double integral of f(x, y) over D is f(x, y)dxdy = ubmit Question

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Q: If r(t) = (t5, t, t²), find r'(t), T(1), r”(t), and r'(t) × r"(t). r'(t) = T(1) = r"(t) r'(t) x r(t)…

A: Given :rt=&lt;t6, t, t2&gt;

Q: Question 4 of 8 View Policies Show Attempt History Your Answer Correct Answer (Used) Your answer is…

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Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t) = (t + 1)³ L{f(t)} =

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Q: Problem 5.3. Solve the following differential equations by regarding y as the independent variable…

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral 00…

A: Graph of a function f(t) is given, we can deduce that the line from x=0 to 1 is linearly decreasing,…

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A: We need to find critical numbers and classify.

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Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. True False

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A: Here, the given function is: f(x)=y=x9-9x

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Q: Find the value of() for a solution (x) to the initial value problem: y"" − 3y" + 4y' – 2y = 0; y(0)…

A: In this question, we want to solve the third order homogeneous differential equation.

Q: Screenshot (1603) Screenshot (1597).png Solve the given differential equation. All solutions should…

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Q: Find a power series for the function, centered at c. 8 5-x £( n = 0 f(x) = C = 1 Determine the…

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Q: 768 on the interval [-20, -10]. Find the H plute extrema for the function on the given interval.…

A: * As per policy only first question is answered. Please refer to the image below

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A: I have solved using two methods

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A: Given: ∫0∞x sin2xx2+3dx

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A: The answer as follows:

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y"" + 3y" - 3y - 2y =…

A: The given differential equation is; 2y'''+3y''-3y'-2y=e-t,y(0)=0,y'(0)=0,y''(0)=1.

Q: Consider the function f(x) = 3x² 10x + 10, 0≤x≤ 6. The absolute maximum of f(x) (on the given…

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Q: Solve the system using Cramer's Rule. 2x + 5y = -25 -x+3y=-4 Find the determinant D (denominator).…

A: Please refer to the image below

Q: Which are the foci of the ellipse represented by 25x² + 16y² = 400?

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 e-{2}- L²s² + n²π² 2_2

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Q: Find T(t) and N(t) at the given point. t x = e¹ cost, y = e¹ sint, et sint, z = zet; t = 0 T(0) N(0)…

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Q: Graph each function and its inverse relation on the same set of axes. Determine whether the inverse…

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Q: ← + Ⓒ Screenshot (1909).png + New ▶ My Drive ▶ Co Computers Shared with me Recent Starred Trash…

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Q: Given the function below f(x) = -75x³ + 200 Find the equation of the tangent line to the graph of…

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Q: Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z…

A: Identify this surface, φ = π/3 in spherical coordinates, and find its equation in x, y, z…

Q: Find curl(5zi + 6xj + 3yk).

A: Our Aim is to find the curl 5z i^+6x j^ +3y k^-(i)

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et,…

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A: The given data is: Lft=Fs and Lgt=Gs, then L-1FsGs=ftgt is true or false.

Q: Determine whether the series Σ=1 (Limit Comparison Test) 2n²+3n √5+n5 converges or diverges.

A: Given :∑n=1∞2n2+3n5+n5

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Q: Use linear approximation, i.e. the tangent line, to approximate 1.3 as follows: Let f(x)=√x. The…

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Q: Use the formula k(t) k(t) = "(t) || ||r' (t)||³ r(t) = 11 cos(3t)i + 11 sin(3t)j + 2tk ||r' (t) = to…

A: The given formula is; κt=r't×r''tr't3 And rt=11cos3ti+11sin3tj+2tk   As we know the Chain rule:…