x2 – 2 (x + 2)(x + 1)² 2 + x +1 1. 2 + (x + 1)2 1 x +2 x +2 (x + 1)2 Option 1 Option 2 2 1 1 2 1 1 x + 2 x +1 (x + 1)² x + x +1 (x + 1)2 Option 3 Option 4

Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A: We have to find the inverse laplace transform.

Q: Question 3 (. whether it is convergent or divergent (show all ) Test the following series your…

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Q: Determine an equation of the inverse of the function y = 5x + 2. A. y= x+ 2 X- 2 С. %3D B. y= 5x- 2…

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Q: Consider f(x) = cos (x) ln(x +2). a. Find the local linear approximation of f(x) at æo (In 2 =…

A: linear approximation of function fx=cosxlnx+2, at point x0=0

Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: Slove this equation -2/x e y dx =1 1 x / dy

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Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: We know that oil form a circular disk on water. And volume of cylinder is V=πr2h Given that…

Q: LDE with Variable Coefficients d²y + 6(x² + x) sin x d?y 6x2 sin x+ 6y sin x – 6 sin x- + sin x- dx2…

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Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = (16/a) on the…

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Q: Use the substitution u = 6x? + 1 to convert the integral fo xeoz+1 dx to an integral of the form L…

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Q: Use implicit differentiation to determine dy/dx given the equation x^5+y^2=−4

A: implicit differentiation to determine dy/dx given the equation    x5+y2=−4

Q: I. Find the Laplace Transform of the given function using the definition of Laplace Transform a.…

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Q: (iii) y= x'e**, y = sin x+eec* (iv) sec x

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Q: 9. Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of…

A: Oil spreads in circle on surface of ocean. Area of circle is A=πr2.…

Q: Find all the second order partial derivatives of the given function. -y? f(x,y) = xye O A. 2f = 2xye…

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-2x. (Use…

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Q: b. d.x Vx4 – 2x2 + 1 3

A: Let's find.

Q: 4) Consider the function g defined by ga, y) = cas (7x Jj )+ logg(x-y) (c) in what dire ction…

A: The given function is: gx, y=cosπxy+1log3x-y. Required formula: The maximum directional derivative…

Q: Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder.…

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Q: the second order partial derivatives of the given function. (x.y) = xye -y O A. 21 = 0;=2xye -Y (2y²…

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Q: 04: S+* + 1)sin z dz =

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Q: 72 a, =6, a,. 1+an

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Q: Find the area of the region described. - 3 The region in the first quadrant bounded by y =x and y= 3…

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Q: 7. The sides of a square are measured to be 4 in, with a possible error of = (4) in. Estimate the…

A: We have to find the possible error and rate of change.     According to our guidelines we can solve…

Q: a) Using the definition of derivative, calculate the derivative of the function of f(x) = /3x +1 (b)…

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Q: dx xVa' +x

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Q: 2. Suppose a wire three feet log is to be cut into two pieces, with each piece to be formed into a…

A: 2) as per our norms we have to write one question at a time kindly repost remaining questions.

Q: 1 an 1 Use the transformation u = 2x+ y, v=x+ 3y to evaluate the given integral for the region R…

A: Given

Q: 1. Use deductive reasoning to show that the following procedure produces a number that is equal to…

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Q: Solve for the second-order derivative of: [(4x3-1)(8x2+6x-3)]3

A: We have to calculate second order derivative of [(4x3-1) (8x2+6x-3)]3   Let us say  Y= [(4x3-1)…

Q: Let R be the finite region enclosed by the curve y = 6x(3 – 2x) and the x-axis. Let V be the volume…

A: See the solution in below

Q: Assume that the radius r of a sphere is expanding at a rate of 10 cm/min. The volume of a sphere is…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: The objective of the question is determine Mn.

Q: Find the following antiderivatives. Cosh sinh r - 1 cosh r dr (a)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Integrate f(x.y,z) = x+ Vỹ - z° over the path from (0,0,0) to (1,1,1) given by C,: r(t) = t i+t°j, 0…

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Q: Find * L-1{ 52-4s+13

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Q: Assume that the number of barbeque dinners that can be sold, x can be related to the price charged,…

A: Given query is to find marginal revenue.

Q: The area under the graph of f(x) = 3x2 between x = 2 andx = k is 504, where k > 2. Find the value of…

A: Given

Q: Find the absolute maximum and absolute minimum of the function f(x)=3sin(x)cos(x) over the interval…

A: We have to find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x)…

Q: If x = t^2 + 1 and y = t^3, then the second derivative is? (Show your complete solution). a. 3/(4t)…

A: Given that,   x=t2+1 and y=t3

Q: On what interval(s) is f'(x) increasing? Decreasing? Explain.

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Q: dy By using implicit differentiation, find dx x.y)-(1.0) for xy + e*» = sin(x +1). (x.y)-(1,0)

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Q: Suppose f(x) = 10 (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum…

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Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

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Q: Find the linearization L(x,y) of the function at each point. f(x.y) = x² + y? + 1 а. (2,1) b. (0,2)…

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Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle…

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Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

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Q: On what instance does the Chain Rule of differentiation applicable? Explain briefly

A: To explain when we should use chain rule.

Q: Cx)= Ex> is add even?

A: We need to determine if the function is even or odd.