Question 8 - Find the radius of convergence and interval of convergence of the series Σ (-3)”.x” √n +1 n=0

Q: 25+1 c) r³-3x²-10x dx

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Q: 10. Prove the identity: 2 + cot² (x) _ 1 = sin² x - csc² (x)

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Q: 1- f(t) = 2t³; 3–f(t)=sinh(2t); 5-cosh (t) sin(2t);

A: Given :1. f(t)=2t33. f(t)=sinh(2t)5. cosh(t).sin(2t)

Q: Let u = (1, 2, –4), v = (-5, 3, -7), and w = (-1,4, 2). Perform the operation u. Type your answer...…

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Q: f(x) = 4x² 8x +3 - x²+x-12

A: The given function is f(x)=4x2-8x+3x2+x-12

Q: +4y= 16t (Laplace)

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Q: Evaluate x² √x² + 25 -2 S dx

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Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. The x-coordinate of the centroid of the…

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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: ㅇㅇㅇ 고 |= 15 n y7

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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: H.W Solve the question deferential equation by using separation varibles dy/dx=sin(x+y)+cos(x+y)

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Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: Evaluate the limit using L'Hopital's rule. Answer should be expressed as a numerical value, with TWO…

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Q: 2. Solve for the volume of solid of revolution formed by rotating the area bounded by y = x² + 2, x…

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Q: the matrix has two eigen vector one of * this(ulkyl gil) 3 2 0 0 -1 0 1 0 2 12032

A: We want to write the eigen vector.

Q: A box with a square base and open top must have a volume of 171500 cm³. We wish to find the…

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Q: Compute the partial derivative of the function * f(x, y, z)= el-roos(y) +2e=1/(1+²)

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Q: In 1950, there were 238,681 immigrants admitted to a country. In 2001, the number was 1,042,425. a.…

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Q: Part III: Approximation and Differentials. (no using of calculator present all manual computations).…

A: To estimate the value of (217)(1/3) by approximation and differentials.

Q: Discuss the relationship between the number of solutions of the following system and the constant k.…

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Q: 2 2) x² + y² - 16x + 18y + 96 = U 0 4) x² + y² + 28x + 28y +376 = 0 2 6) x² + y² - 16x-20y+128 = 0 0…

A: Solution is here

Q: To produce x units of a religious medal costs C(x) = 13x + 102. The revenue is R(x) = 30x. Both cost…

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Q: 2-f(t)=3e-²¹. 4-f(t)=2 cos(3t). 6-f(t)=cos't-

A: Answer highlighted 3 questions(2,4,6)

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5x - 4x²…

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Q: Find Vf at the given point. f(x,y,z) = x² + y² -32² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+ (8)j + (-30)k…

A: Topic = Derivative

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

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Q: Write an equation of the line perpendicular to the line y = 3x − 7 at (5, 8).

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Q: 16. J x² 4 + x² dx

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Q: area of a rectangle is fixed at 60 square meters. The base is increasing at a constant rate of 2…

A: Given the query is to rate of change of height.

Q: Find lim (11) O limit does not exist Oe¹-2 Oe¹-4 O2 Other 1/2

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Q: determine all inflection points of x^4 + x^2

A: Let,  f(x)=x4+x2 Now, f'(x)=4x3+2xf''(x)=12x2+2

Q: 12

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Q: 13- Find Gamma Function for (a)T (5); (b)r(7):(c)r 2

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Q: dy Assuming - 9x3 + 7y2 – 2xy = 0 defines y as a differentiable function of x, use the theorem dx =…

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Q: A light shines from the top of a pole 15 m high. A ball is dropped from the same height from a point…

A: solution is here

Q: Find the derivative of the function at Po in the direction of u. x-y g(x,y)= xy+2 Po(1,-1), u=12i+5j…

A: Given :g(x,y)=x-yxy+2u=12i+5j

Q: Use Lagrange multipliers to find a relative minimum function value of fif f(x,y,z)= x² + y²+ z² with…

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Q: 8. y = log x-1 x+1

A: Let's find second derivative of given function.

Q: 2 2a 2b + c = -2 a + b3c = 3 a 3b + c = -5

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Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: Given problem:- A manufacturer is planning to sell a total of 500 machines to both foreign and…

Q: x4 dx 2 2 (x² +9) ² 3 = 3 WIX 2 Arctan là + 51]+c 4 (x249)

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Q: Evaluate (2a³y +9y³)dA, D is the region bounded by y 33522 a. 5 Ob. 4811 5 C. None of the choices.…

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Q: © Evaluate A2, where A = that al+bA + CA² = 0. 2 3 -5 5), and find a, b, c E R, not all zero, such

A: A = (2  -5)        (3   1)   A2 = (-11  -15)         (9      -14) aI +bA +cA2 = 0 ( a  0)   +  (2b…

Q: 2) x² + y² - 16x + 18y +96= 0

A: Here we havw to convert standard form,  2) x2+y2-16x+18y+96=0

Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship…

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Q: Using Trapezoidal method ²x³dx for n=4 is equal to Blank 1 (use 2 decimal places with proper…

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Q: Equation Conversion from Polar to Rectangular Coordinates r² = x² + y² r cos 0 = x 2. Convert each…

A: As per Bartleby guidelines rule I am answering only first three questions.

Q: 10. y (e-3x+4 +2)/(e2+3x +1)

A: The given function is ; y=(e-3x+4+2)/(e2+3x+1).

Q: 15. Iv X V9 – x2 - dx

A: We want to integrate the given function.