Evaluate the following integral. e2. 1 In ³ (x²) X dx

Q: In Exercises 13-16, find and sketch the level curves f(x, y) = c on the same set of coordinate axes…

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Q: Question 21 Determine the derivative of the following curve: x² + y² = 5 Oy = -√2 Ov=√ Od = -√√…

A: Explanation of the answer is as follows

Q: Find the indefinite integral. (6x + 1)-9dx

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Q: ✓5. 4y³(x² +4) dx + 4xy¹ = (x² +4)² dx

A: Given differential equation:- 4y3x2+4dydx+4xy4=x2+42

Q: 4) Find the equation of the tangent line to the function f(x) = 3 at x = 1. Round the slope to one…

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Q: Find the centroid of the region lying between the graphs of the functions ye and y = 1 over the…

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Q: Use interval notation to represent the separate intervals where 2x + 5 will be non-zero:

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Q: y = 5x³

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Q: Find the derivative, y', of the function y = sinh(lnx) - cosh(lnx) O y = 0 O y = 1 Oy = 2/ 0 y =…

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Q: Evaluate the following integral using integration by parts. f10te' dt OA. 10te¹ + (10te¹) dt OB.…

A: Given query is to find the value of the integral.

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: Let x m be  length and y m be  width of rectangle  Perimeter of rectangle=2x+y m Area of…

Q: Step 3 Now write the derivative in terms of x by recalling that u = -3x + 7 and v = x + 7. du 1 +=…

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Q: Consider the following. 7x²y³ = 8 (a) Find y' by implicit differentiation. 14x 3y y' = (b) Solve the…

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Q: r(t) = (0,8 cos³ 10t, 8 sin³10t), ≤ t ≤ 4

A: I am attaching image so that you understand each and every step.

Q: Step 2 Now write the derivative in terms of x by recalling that u = x³ = x + 8. [eu] = (eu) du dx…

A: I have solved step by step in detail....go through the solution

Q: Evaluate the double integral by first identifying it as the volume of a solid. 12 18 (8 - 4y)dA, R=…

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Q: 100 56. Σ (3k + 4) k=1

A: Note: Since the student has mentioned to solve only question no. 56, so we are solving accordingly…

Q: In getting the derivative of a variable raised to a variable y = [f(x)](2), which of the following…

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Q: i. sin³ (r) dr dx ii. (tan(x) dx

A: Given query is to find the value of the integral.

Q: Differentiate y = 6 + sin x x + cos x

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Q: Find the solutions of the following IVPS or DE. a. y" — 4y' + 4y = e²x, b. y" - 2y = e2²x +3, y(0) =…

A: See the details solution in below

Q: Sketch the level curve of the function h(x, y) 10+ 9 8 7 6 5 4 3- 2 + -10 9 8 7 6 5 4 3 2 1 + -2 3 4…

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Q: 20. Evaluate the limit or show that the limit does not exist. Show proper work. sin y cos y ye (a)…

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Q: Given a first-order differential equation: /1 + x² dy-ydx = 0 a) What is the best solution method in…

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Q: D Question 25 y sin 2x + cos 2y = ax; Oy = Oy = 0% O y = O✓ = y a-2y cos 2x sin 2r-2 sin 2g a+2y cos…

A: To determine the derivative of given function.

Q: Question 5 Determine the derivative of tan(e) O e sec(e) tan(e*) 25+2 1+e²² O e sec²(e) O sec(e)…

A: To determine the derivative of tanex.

Q: 25 Determine the surface of the solid formed by revolving the upper half of the circle x² + y² = p²…

A: According to bartleby guidelines for multiple question I can answer the first question. Thankyou.

Q: Find the second derivative (y") of the given function: y = ln (7- x³) O-3x(14-x²) O-3z(14+x³)…

A: Given:  y=ln(7-x3)   To Find : Second derivative of the given function

Q: Are 2 -baz

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Q: Find the absolute maximum and absolute minimum values of the function f(t) = √t · (3 – t) on the…

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Q: 2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the…

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Q: A rectangular poster is to contain 162 square centimeters of print. The margins at the top and…

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Q: If a and h are real numbers, find the following values for the given function. The function is…

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Q: Find the area of the region bounded by the curves y = xe -0.4x Area = x = 5, and y = 0. >

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Q: Evaluate the following integral using integration by parts. In 22 xe Xex dx In 22 S Xex dx = 0 (Type…

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Q: Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x² y³ - ky)dy = 0 a) Solve…

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Q: 66. 1 - 1 2 + 2 4 68. + 5 25 1 4 + T 8 125 +

A: Question no. 66 & 68 solved

Q: r(t) = Make a plot that verifies your result. = St²+2t2 if t≤ -3 {at + b if t> -3 Find a and b such…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Let f(x) f(g(x)) = g(f(x)) 30 C Question Help: - 4 Find the following functions. Simplify your…

A: Given query is to indicated composite function.

Q: A particle moves along the curve implicitly defined by xy¹ - yx4 = x-y2. When the particle passes…

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Q: Find the area of the region bounded by the curve y = x² - 6x + 7 and the line x + y = 3.

A: The curves are y=x2-6x+7 and x+y=3

Q: Question 26 Find the second derivative (y") of the given function: y = e² sin z *)(2(- sin x)) e²…

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Q: Given: y = 5 (cosh log )², find y' (cosh² O g = =|sinh 2 log = ]5 sh®log }} O 5 O ý =−}(m& )[sinh 2…

A: The objective of the question is determine the derivative of the given function and choose the…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: solution:-the region bounded by 27y, x=0 and y=3 rotating about y-axisusing cylindrical shell…

Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

A: Graph:-

Q: Evaluate the double integral. 116 4x². (+² + 2y) dA, D is bounded by y = x, y = x³, x ≥ 0

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Q: 1. Find the double integral over the region R bounded by the functions. Choose the more convenient…

A: To find:- ∬Rx3y2dA ; y=x,y=0,x=1 ∬xeydA ; y=x,y=0,x=1 ∬RxydA ; y=x2+1,y=3-x2

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 6t+ 6…

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Q: The average price of a two-bedroom apartment in downtown New York City during the real estate boom…

A: Topic- exponential function and derivatives    We are given, The average price of two bedroom…

Q: 1 2 ső ső (x + y) dydx 0 O none is correct O-3 02 0 3

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