Find the radius of convergence and interval of convergence of the series (-3)"x" √n+1 n=0

Q: Which of the quantities is nearest to the value of * exp 0.003 1.001 cos(0.002) ? O 1 O 1.001 O…

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Q: Consider the vector-valued function In(2t + 1) sin t R(t) = î+ t t Redefine (t) such that it is…

A: we say the R(t)  is continuous at t=0  if limt→0 R→(t)= R(0)

Q: Function: f(x) = 6 - 12x + 2x3 Find: Critical points, maximum, minimum

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Q: 3. f(x) = 3x-7

A: Topic:- derivatives Note :- as per our guideline if more than one question uploaded than only first…

Q: 1. Consider a point in Cartesian coordinates given by (3√/3, -3, -8). (a) Find a corresponding…

A: Given, (x,y,z)= (3√3,-3,-8)

Q: In the partial fraction decomposition for some numbers A, B, and C. Find the value of B? -x²-x+2 C A…

A: On solving this we will get:  B= 1/2

Q: 2 Consider the vector-valued function R(t) with Ả'(t) = (sec²(t – 1), √t' (a) Find R(t) given Ả(1) =…

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Q: Find: y = arctan = 1 O a. none of these O b. 0 с. O d. 177 O e.

A: Given;  y=tan-1[(x+1)/(x-1)] at x=1.

Q: If the function u = 2e^u e^2u 1/2 Other: In (2² +2²¹²) then ro + you is 4

A: First we calculate partial derivative.

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

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Q: Find f such that f'(x) = f(x)= f(16) = 21.

A: Topic:- application of integration

Q: Solve of the following deferential equations r sin 0d0 + (r.³ – 2p2 cos+cos) dr os 0) dr = = 0

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Q: Use the equation to name each of the characteristics listed. Make sure to use proper notation and…

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Q: 4. x = 3 + 4 sine, y = 3cos0 - 4

A: Given: x=3+4sinθ, y=3cosθ-4 dxdθ=ddθ3+4sinθ = 4cosθ dydθ=ddθ3cosθ-4 = -3sinθ

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: Evaluate x² √x² + 25 -2 S dx

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Q: Find the volume of the parallelepiped determined by the vectors (0, 4,-5), (2, 0, 5), and (-1,3,0).

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Q: Set up the integral representing the area of the region between the curves x = -1, x = 4, y = 2x -…

A: Consider the figure

Q: ~ f ² f (x) dx = -5 and Given than (A) None of the given choices B) √ f (x) dx = 8 © [²] f (x) dx +…

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Q: Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the…

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).

A: We have to find dy/dx.

Q: 2. Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal,…

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Q: The height and radius, respectively, of a cylindrical tank is 5 m and 2 m. If the tank is full of…

A: Given

Q: In solving for the antiderivative of f(x)= using trigonometric substitution, f(x) dx is transformed…

A: given solution is correct,

Q: An aircraft sets a course with a certain bearing and at a speed of 500 mph. A horizontal wind…

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Q: f ƒ (a,b, c) = cos (ab) + sin (b) + c where ƒ ((2, 73,7)) Evaluate af да (1,3,7) O Option 3 T√3 12 ل…

A: Topic:- application of partial derivatives

Q: (Inverse Trigo, Higher Order Derivative, Chain Rule) Directions: Find the derivative of the…

A: The given problem is solved below in detail.

Q: Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) 4 with initial vector

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Q: 1. Consider a point in Cartesian coordinates given by (3√//3, -3,-8). (a) Find a corresponding…

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Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: S x cos √x² +4 V √x² + 4 dx

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Q: The radius of convergence of the series Place) (-1)" (n!) 0 3-6-9. (3n) (2x-1)" is equal to…

A: To find the radius of convergence of the given series.

Q: 2. y = (x + 1)2 and y = -x + 1

A: Topic:- application of integration Note:- as per our guideline if more than one question uploaded…

Q: 5. The region is bounded by y = x³, y = 2x + 4 and y = -1. Then, Area region = [*f(x) dx + [[g(x)…

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Q: x² In solving for the antiderivative of f(x)= √√4-x² using trigonometric substitution, f(x) dx is…

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Q: Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: Given r=2-3cosθ in the  polar coordinate system We need to find "r" for all the angles     For θ=0,…

Q: Which ONE of the following statements is TRUE with regards to lim (x,y) → (0,0) sin (xy) x² + y²

A: The correct answer is option D.

Q: f(t)=sin(-t)- f(t)=1-cos(wt). soo.(10){SI=(1)f

A: We have to find Laplace Transform of given function.

Q: In a laboratory experiment, the population P of a microorganism is found to satisfy the differential…

A: The given problem is solved below in detail.

Q: Can you pls show me how did you get this? ln x = -6x  x = 0.2387

A: Let's solve.

Q: x² 8. (x) tan 3x+cot 3x 9.f(x) = 2 sin 4x cos 4x =

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Q: Consider the spherical equation given by p = 4 cos sin p. Determine its corre- sponding equation in…

A: Given

Q: (a-x)² (a-y)² (a-z)² Express (b-x)² (b-y)² (b-z)² as a product of two determinants and hence…

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Q: The interval of convergence of the series Σ(√n+1-√√n) (x+2)" is given by A=0 A-3≤x<-1. OB-3<x≤-1.…

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Q: Find and classify all critical points of the function f(x, y) = x³ + 2y4 - In(x³y³)

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Q: The force on the triangular plate that is submerged in water as shown below waters surface 6m 4m is…

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Q: What is the corresponding Cartesian coordinates for the polar point (-4,-)? (2√3,-2) (-2√3,-2) O…

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Q: 2 I 2 Vr +25 dz

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Q: 3. Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: given isr=2-3cosθ