Find the area of the surface obtained by rotating the curve about the y-axis. 1 1 y=-x--lnx, 1≤x≤8 4 2

Q: Find the Taylor polynomial p₁(x) for f(x) = ln (3x) at x = 1.

A: Given: fx=ln3x To find Taylor polynomial at x=1 We know that ddxlnax+b=aax+b

Q: Question 1 equation : y cost + 2te³+ (sint + t²e - 1)y' = 0. Consider the differential a) Show that…

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Q: Which one of the differential equations is exact? Select one: O None of the others. ○ (4xy² + 2xy)…

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Q: The differential equation exy' + 5x³y = (3x - In x)y-³ is a Bernoulli's equation. Select one: True O…

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Q: Evaluate Definite Integral √x ³² (2x² + 1) ªdx 2.

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Q: ind the equation of the tangent line to the graph of the function f(z)=(22+ 10) (-2) at the point…

A: Given query is to find equation of the tangent.

Q: Find the volume of the solid bounded by the hyperboloid z² = x² + y² + 1 and by the upper nappe of…

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Q: Use what you have learned in Calculus II to find the area of the triangle made up of the points…

A: Let's find area of hexagon.

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = x² from…

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Q: dy dt + y cos(2t) = 0 ; y(0) = 1

A: Topic:- application of integration

Q: A. Evaluate the following: NO Differentiation 1. lim(x³ - 2x² + 3x-1) x->2 2 lim (4 + 3r²-2r+5)

A: To evaluate the limit of the given function

Q: The equation 2 dy x² dx is a first-order linear differential equation. Select one: O True O False -…

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Q: 2) Consider the DE: (2xy − 6x²)dx + (x² +9)dy = 0 - A) Determine whether the DE is exact or not,…

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Q: Calculate the test-statistic, t with the following information. n₁ = 45, x1 = 2.52, s₁ = 0.57 n2 =…

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Q: (1) Suppose you lift a stone that has a mass of 5.9 kilograms off the floor onto a shelf that is 2.5…

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Q: Find the positive integer that minimizes the sum of the number and its reciprocal.

A: Let the positive integer is x ( x > 0) The sum of the number and its reciprocal is f(x)  (let),…

Q: (d) fbx ²²+1 dr br

A: We can evaluate the given integral by using the substitution u = ax2 + 1

Q: x + y - 4 (x,y)-(2,2) √√x+y-2 lim O Ninguna de las anteriores 00 04 O-4

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Q: Graph the function, not by plotting points, but by starting from the graphs below. h(x) = 6 - 10x y…

A: Let's draw the graph of given function.

Q: Consider the DE: (4x + 6y)dy + (-2x + 4y)dx = 0 A) Using only the notations followed in class, Find:…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (b) 542+7 dx

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Q: Consider the image below. -12-10-8-6-4 4 2 FJ -16-14-12-10-8-6 A)-2 B) 0 8+ 64 A)-2 B) 0 41 24 0 -2…

A: Given that graph of fx and gxSolution :10.limx→-3+ fx+gxlimx→-3+ fx  +lim     x→-3+ gx-2+2=0option B…

Q: Question Find the Taylor polynomial p3(x) for f(x) = 4e at x = 1. Sorry, that's incorrect. Try…

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Q: estion Consider ta linear differential equation xy' + 3y = 2x³. (a) Find the integrating factor of…

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Q: Prove that for all values of λ and u, the planes 4x 3y 5+μ a b 2x y 2z x 2y 2+2+²-1+2 ² 2 ²-2) = 0 -…

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Q: Fill in the blank. The One-to-One Property of exponents with natural base e states that if ex = ey,…

A: Given that  e(x)=e(y) ex=eyThe one to one property of exponent states that is base is same then…

Q: Without​ graphing, determine whether the following equation has a graph that is symmetric with…

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Q: . Consider the differential Question equation : y cost + 2te" + (sint + t²e" - 1)y' = 0. a) Show…

A: The given differential equation: ycost+2tey+sint+t2ey-1y'=0.The given differential equation can be…

Q: Find an equation of the tangent line to the graph of f at the given point. f(x) = √√√x, (25, 5) y =

A: Given query is to find the equation of the tangent.

Q: In order to solve the following Bernoulli's equation dy dx we use the substitution e+3 Select one:…

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Q: Question 2 differential equation 2 = y² + ¾/7 y y² + y = 1: Consider the following a) Is the given…

A: The given differential equation is:1ty'+2t2y=t4e-4ty-3

Q: Where is the function f(z,y): cus y sin z cos y I #0 z=0 continuous? Prove your answer

A: The function is continuous if limit exist and equal to value of function

Q: Use the graph of the function f shown in the figure to the right to estimate the indicated function…

A: Given graph:-

Q: Integrate f(x, y, z) = 3x²y² over the solid bounded above by the cylinder y² + z = 9, below by the…

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Q: Find the local and/or absolute maxima and minima for the function over the specified domain: y=x+1|…

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Q: What is the general solution to tan a (csc x+2) = 0?

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Q: Find f'(a). f'(a) = f(t) 6t + 2 t + 3

A: As per the instruction, we will be answering the first question. Given: Now,         f'(t)=6t+2t+3'…

Q: Question 1. equation : y cost + 2te³ + (sin t + t²e³ − 1)y' = 0. 1: Consider the differential a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE. Enter…

A: We have to find the vertical and horizontal asymptotes.

Q: What is the symmetric difference of two joint sets equivalent to? complement of the set intersection…

A: Solution is given below:

Q: O 8e²-4e-4t ○ 4e²¹-8e-4t Ninguna correcta • u = x(4+ y²), x = e³t & y =

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Q: 6. Find Indefinite integral. Show all yo √(x² + 5*) dx 7. Evaluate Definite Integral .Show all your…

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Q: an Indefinite Integral. Show al S x ²³= 3x² + 5 X-3 d

A: Topic - indefinite integral We are given ∫x3-3x2+5x-3dxwe know that∫xndx=xn+1n+1+C∫1xdx=ln(x)+C

Q: Sketch the curve of the following:  y = 1 + 1/x + (1/x2)

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Q: The answer given in my answer sheet is 108 square centimeter.

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Q: Suppose F(5) = – 7, F(9) = 4, and F'(x) = f(x). 5 9 6f(x) dx =

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Q: 08/298 1 4:2

A: Topic:-  Binary number system

Q: Suppose F(3) = 3, F(7) = = -9, and F'(x) = f(x). Also suppose G(3) = 2, G(7) = 5, and G'(x) = g(x).…

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Q: Find the absolute extremum, if any, for the following function. f(x) = 4x - 7 Select the correct…

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Q: Using a proper substitution, Bernoulli's equation dy dx - 5 xy = - 4 x²y4 will be reduced to the…

A: Please see the below picture for detailed solution.