(1) [ Evaluate the indefinite integral by substitution: a+bx² dx 3ax+bx3 (2) / sec³xtanxdx T

Q: ff. W Ex] Let f(x) = 4x²+2x²+x+3 and :f(x), g(x) € 75[x] f(x). g(x). g(x) = 3x² + 3x²³² + 3x² + x…

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Q: Which of the following statements are FALSE about the method of variation parameters? I. II. If y₁ =…

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

Q: (1) ₂ (3+√4-x²) dx -2

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Q: dy ssuming 5x³ +9y² − 4xy = 0 defines y as a differentiable function of x, use the theorem == dx Fy…

A: Given query is to find the derivative at indicated point.

Q: y=1/x²₁ y = 8x₁ y=x/8

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Q: The solution of the equation below can be represented as y(x) = yn (x) + yp(x). y" + 3y' - 4y = 3x +…

A: To find the corresponding particular solution of the given differential equation.

Q: An inner city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

A: here lets assume width of rectangle is b length of rectangle is 2b width change is db/dt = 43 m /…

Q: Give the domain and range. Then, use the graph to find (a) f(-2). (b) f(0), (c) f Ay 40 & M 2 X and…

A: Answer: The solution is given below:

Q: Draw the graph of y = 3x2 + 6x − 24 and label its minimum

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Q: A lighthouse is on an island 500 meters off shore. The lighthouse beam makes a full turn every 9…

A: A lighthouse is on an island 500 meters off shore. The lighthouse beam makes a full turn every 9…

Q: Find the following integrals a) f_d dx x√In x

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: +4y= 16t (Laplace)

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Q: Solve the following differential equations: 1 √1-3x (a) -dx + sin y cos 2y + 1 dy = 0 (b) x²y + x³…

A: I am attaching image so that you understand each and every step. Here "c" is integration constant.

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x)=80x−0.5x2 and…

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Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

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Q: 3. Use appropriate differentiation techniques to determine the first derivatives of the following…

A: see below the answer and calculation

Q: Find the area enclosed by r² = 4 sin 20.

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Q: Which of the following integrals represents the area inside the curve r = 3 + 2 cos 0 and outside…

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Q: let W = (x₁ +₁2) be jointly discrete. valid joint pdf a random vector. Contract of W (with atleast…

A: answer is in next step

Q: * Integral use to solve if series converges or diverges, give example if true or false

A: follow the procedure given below.

Q: Classify the following differential equation: Second order, nonlinear Nonlinear, homogeneous Linear,…

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Q: f(x) = 4x²8x +3 x ² + x - 12 2

A: Given.

Q: What is the corresponding Cartesian coordinates for the polar point (-4,-)? (2√3,-2) (-2√3,-2) O…

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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: The sum of two numbers is k. Find the minimum value of the sum of their squares.

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Q: f(t)=sin(-t)- f(t)=1-cos(wt). soo.(10){SI=(1)f

A: We have to find Laplace Transform of given function.

Q: x² + 8x - 9 x1 x³2x² - 5x + 6 t³7t² + 16t - 12 t4 - 4t³+ 4t² 4. lim 5. lim t-2

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Q: J (u-2) (u+3) du

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Q: A balloon is released fromthe ground 100 meters from an observer.The balloon rises directly upward…

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Q: 15. Iv X V9 – x2 - dx

A: We want to integrate the given function.

Q: Find the following improper integrals a) dr b) fodr

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Q: 2. Consider the spherical equation given by p= 4 cos sino. Determine its corre- sponding equation in…

A: givenρ=4cosθsinφ

Q: where y is considered to be a function of . In this exercise, you will determine whether or not y =…

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Q: What type of limacon is the graph of the polar equation given by r = √3+ cos 0? O Limacon with a…

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Q: Question 10 : Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It…

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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: Evaluate. Then interpret the result in terms of the area above and/or below the x-axis. [(x²-3x) dx…

A: Here, we have given a definite integral and we have to evaluate it we have to find what amount of…

Q: */3 Jπ/4 cscxcotxdx

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Q: 3. Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: given isr=2-3cosθ

Q: 25+1 c) r³-3x²-10x dx

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Q: Question 8 The value of x for which the series Σ QAX<2 or 4<x. OB2<x<3 or 3 <x ≤ 4. OC. None of the…

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Q: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the…

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Q: Use of an Auxiliary Variable Solve the equation. The sum of two positive numbers is 2. Find the…

A: see below the calculation

Q: [²³ 0 ✓1+13xdx

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Q: What is the area of the region enclosed by the graph of r² = 3 + cos 0? √ √3+ cos e de √(3 + cos 0)…

A: We have to choose correct option.

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

A: We first sketch the given region using a graphing calculator.  We will consider the graphs about…

Q: 2. Consider the spherical equation given by p = 4 cos sin p. Determine its corre- sponding equation…

A: The equation in spherical polar coordinate is ρ = 4cosθsinϕ                             .......1 To…

Q: L₁ |x|dx

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Q: Find the value of (D) solve in detail 1219 = 20.88 * (0.015/60)1.85 4.87 D4 Ans. D= 0.0186

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Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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