Solve the given initial-value problem by finding, as in Example 4 of Section 2.4, an appropriate integrating factor (x² + y27) dx = (y + xy) dy, y(0) = 1

Q: Solve the following initial value problem. y"-2y' + 2y = 7x+1; y(0)=3, y'(0) = 0

A: The given initial value problem,y''-2y'+2y=7x+1; y0=3, y'0=0

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Use finite approximation to estimate the area under the graph of f(x) = 6x² and above the graph of…

A: I have appended the formula used in the solution part of the question

Q: + 192t +9. Find its maximum height. - 16t²+ The height (feet) of an object launched in the air t…

A: Second Derivative Test: If x=a is a critical point of the function f(x) and f''(a)<0 then f(x)…

Q: ✓ z Find J 1+sin -cos COS In sin 2+cos z 1+sin-z In | In 1+cos - 2 1+0 +C +C +C

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Q: Calculate the discount on one bike if they decide to buy 10 bikes at the same time.   1.3.2…

A: This is basic algebra problem

Q: 16 sin²x cos²x dx

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Q: Use the price-demand function below, to answer parts (A), (B), and (C). p(x)=85-3x 1 ≤x≤25 (A) What…

A: Given data÷

Q: e. f. g. 1 2 [x² + 5x ²3³/dx S² น u² 2 + 3 du 0 1 [²x(x² x(x² + 5) dx 0

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Q: Use indirect proof to show that if n is an integer and n^3 + 5 is odd, then n is even.

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Q: Find the derivative of the function f(x), below. It may be to your advantage to simplify first. f(x)…

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Q: Find the "actual" solution (x,y) for the following problem. max_x2y² subject to 2x + y ≤ 2 x20,y20…

A: Given:    2x+y≤ 2 , x≥0 , y ≥0    Max - x2y2

Q: Which of the following integrals would yield the area of the region below? 2 x=y 3 1 0 x = 8y 00 8

A: A detailed solution is given below.

Q: Evaluate: So fixy³ dydx

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Q: Find the integral which represents the total mass of the triangular region below (see the picture),…

A: Total Mass = ∫∫R δ dA ; where, 'δ' is the density . Note : As per our Guidelines , we can solve…

Q: Problem 11. Discuss the function f(x) = in terms of its concavity, inflection points, and local…

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Q: Solve the following initial value problem. y+y"=6x+8e; y(0) = 1, y'(0) = 0, y''(0) = 1 The desired…

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Q: a. b. C. [(x² + 2x³ + 4x + 10) dx [ 6xe*² dx [ In x dx

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Q: se the Ratio Test to determine if each series converges or diverges. 3n+2 ΙΣ Inn 2 n=2

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Q: The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10…

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Q: 3) Suppose that in a certain fish hatchery, the fish population is modeled by the logistic growth…

A: This is a problem related to exponential model function. Based on the general formula and concept we…

Q: Use the given transformation to evaluate the integral. J (8x + 8y) dA, where R is the parallelogram…

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Q: Additional Activities What function will you differentiate to get each function? 3. g(t) = -3t2 +…

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Q: Q3/ Find the IVP for the differential equation. x²y" - 3xy² + 68y=0, that satisfies the -зху!…

A: Follow the procedure given below.

Q: egrals: 12+5-6 2.J xinxd

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Q: Find a particular solution yp of the following equation. Primes denote the derivatives with respect…

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Q: f cos² x dx

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Q: x³ + 3x² + x +9 3 (x² + 1)(x² + 3) s dx

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Q: a) Let an be an arithmetic sequence. If as 94, a6 = 85, find the common difference d and the formula…

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Q: the convergence and divergence of the following S vergent series. b) Σ=13*51-n

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Q: a. Show that f has a removable discontinuity at x = 3. f(x) = x²7x+12 x + 2 x = 3 b. Redefine f(3)…

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Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

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Q: A person starts walking from home and walks: 2 miles East 5 miles Southeast 6 miles South 6 miles…

A: Use vector concept

Q: 7 Find (x³ +2x) dx S. x²+4 None of the Above √√√√x² + 4(x³ - 2) + C √√√x² + 4(x² − 2) + C - O√√²-4…

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Q: Solve the given differential equations: dy 1. 2+y² dx

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Q: Numerical Response #7: The arc length of a circle of radius 15 cm with a sector angle of 110°,…

A: We have to find Arc length of given circle.

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Q: 41. Two straight roads diverge from an intersection at an angle of 60°. Two cars leave the…

A: Above question is solved.

Q: S Solve (2-2)² 3 3 ln | x − 2 | −³₂ + C 2 ln | x − 2 | |-2| − — ²/₂ + C None of the Above 2 ln | x −…

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Q: Evaluate the integral. (Use C for the constant of integration.) /1+√x ox dx

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Q: fcx) = sinh x X il 10 - 2 (1+X+X/21 + X/31 + -)-(1-X + X²/21 - X/31 --) 2 3 +2 5 2x+2 31, 2 3! 51…

A: We know, coshx= [ex+e-x]/2 and emx=1+mx+m2x22!+m3x33!+... for any real number m

Q: Find the rate of change of the surface area of a hemisphere with respect to its radius. a. When the…

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Q: Numerical Response #2: Bonnie is investigating the polynomial function P(x) = ax + bx³ + cx² +dx+e…

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Q: c- Show that the following limit does not exist (x² - y²) lim (x,y)-(0,0) x2 + y² 2

A: Given ; lim(x, y) -(0,0)[(x2-y2)/(x2+y2)]2.

Q: e the graph of f(x) is given. Describe verbally how the graphs of the following functions can be…

A: Graphical transformation

Q: Evaluate the integral of ₁dx for P > 1, and determine whether it is convergent or divergent.

A: SOLUTION-

Q: Use spherical coordinates. Evaluate SSS √x² + y² + z² dv, where E lies above the cone z = √√x² + y2…

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Q: Evaluate: fr² cos 3rdr

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Q: 1) y" + 4y = 4 sec(2x)

A: Since multiple questions are asked, I am answering the first question.

Q: Find the exact value of the trigonometric function of using the given format: 5п Let then is in Q…

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