Draw the given optimization problem and solve. Find the dimensions of the closed cylinder volume V=16pi that has the least amount of surface area.

Q: Find the first derivative f' and the original function f. ƒ"(x) = cos(x), s' () = 5. ()=4 f' (Use…

A: Topic- differential equations

Q: 8. Analyze the graphs of f', then list all intervals where f is increasing or decreasing. f'(x), 1-…

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Q: Determine whether the statement is true or false. If f and g are discontinuous at x = c, then so isf…

A: 1. If f and g are discontinuous at x=c, then so f+g. 2. If fx is continuous at x=c, then so is fx

Q: Using the trigonometric substitution x = 6 cos 0, 0 < 0 < π, the integral √36-x² x² In cos 0 + C O…

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Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve r(t)…

A: This question can be solved using the concept of vectors and derivatives.

Q: Suppose you have 1640 meters of fencing available with which to build three adjacent rectangular…

A: answer is in next step . please give a like !!

Q: Work Problem I answers. 1: Write step by step solutions and justify your 1) [ ] A bacteria culture…

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Q: The general term of the sequence is Select one: O True O False 1, an = 1-1 1 (-1)"+1 ,n21

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Q: Find the limit. Ilm (x + 7)

A: We can find the limit as below.

Q: ion (4 points): Duble integrals below are equ 3x 1 dydx = 48

A: Please refer to the image below

Q: Find the general solution of the differential equation. y(4) +12y" + 36y = 0. NOTE: Use C₁, C2, C3,…

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Q: ! -<0<, an integral was transformed to the form 11 -do. sin 0 cos³0 In terms of x, the integral I is…

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Q: i) Find the exact length of the curve 1 15 4x3 y y = ii) Find the exact area of the surface obtained…

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Q: Evaluate the two integrals given the graph. The two parts of the graph are semicircles. [₁50x 1°…

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Q: 11. (a) Find F'(x) using the limit definition of the derivative if F(x) = F'(x) will result in zero…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: Use the alternative form of the dot product to find u. v. ||u|| = 50, ||v|| = 25, and the angle…

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Q: If sin 0 O a) cannot be determined Ob) / 09-1 Od) -42 4√2 O e) 4√2 9 -- and is in quadrant IV, find…

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Q: True

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Q: Sketch the plane curve. r(t) = tr + t2j, [01] y 1.0 0.8 0.6 0.4 0.2 y 1.0 0.8 0.6 0.4 0.2 0.2 0.2…

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Q: Determine the equation of the parabola whose graph is given below. Write your answer in General…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t…

A: Topic = Functions

Q: (a) Find the equation of the tangent line to the curve y = x² at x = 1. (b) The line in part (a) is…

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Q: The elimination method was used to solve the following system of equations: x²-y=-4 x² + y² = 18…

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Q: Find the average rate of change of the function f(x) = x² - 2x + 3 between x = -2 and 2 = 4. Type an…

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Q: . Use separation of variables to solve the differential equation explicitly for u. du dt = 4 + 4u +…

A: topic:- differential equation

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: 3).   Draw the directional field for the differential equation. y' = 3y + xy

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Q: Find the equation of the tangent line and the normal line at the point corresponding to the given…

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Q: nd barely audible to the human ss the formula so that the expression in parentheses is written as a…

A: topic:- algebraa

Q: X-0 X X f(x) -0.1 -0.01 -0.001 0 ? 0.001 0.01 0.1 Use the result to estimate the limit. Use a…

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Q: Use the method above to find a second independent solution of the equation ty" - y' + 4t³y = 0, t >…

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Q: A particle is moving with the given data. Find the position function, s(t), of the particle. [Note:…

A: Solve the following

Q: (A) C B) a (A) a B d с dx ex√4-e²x the integrand is transformed into? (a) cos²0 (c)-sin²0 (b)-sec²0…

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Q: Find the shaded region in the graph. 4 3- NO 2 1 X = y=2 y = cos x + 1 π/6 E|M 3 πV3 π: ….. The area…

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Q: d the general solution of the following differential equation. y" + 7y' + 12y = 0 E: Use c₁ and c₂…

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Q: -00 6w³ 2 (w² + 1)² -dw

A: Use the properties of definite Integral to solve the given integration.

Q: 3 X The double integral ³ x dydx has a rectangular region. Select one: True False

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Q: a. In a geometric progression the sixth term is 8 times the third term and the sum of the seventh…

A: nth term of the Geometric progression , an= arn-1. Note : As per Our Guidelines , we can solve…

Q: Find the area of the region enclosed by the curves y² - 5x = 9 and x - y = 1. The area of the region…

A: Please refer to the image below

Q: y = -x² + 13 and y = x² + 5

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Q: Find the area between the curves y = e Area - 0.7x and y = 1.3x + 1 from x=0 to x=2

A: The area between the curves y=e-0.7x and y=1.3x+1 on interval 0, 2.

Q: Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1,1₂ = -4,13 = 7, and A4 = - 7. Use the following…

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Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: Using decomposition into partial fractions, the following integral is equal to s 27 2x + 1 3x3 - 27x…

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Q: Find values of x, if any, at which the given function is not continuous. f(x) = Of is not continuous…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ TACHY 1. (D³ - 5D² + 3D + 9)y = 0 2 (D3 D2 1

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Q: solve the following diffrential c) x²(y+1)dx+(x²-1)(y-1)dy=0

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: The marginal cost of printing a poster when x posters have been printed is dollars. Find c(100) –…

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