Homogeneous Equations Obtain the family of solution of the equation (x2 + y2)dx + xydy = 0

Q: Consider the following function: (x+1)² if x ≤3 -2x+22 if x > 3 f(x) = x) = {(x + 1)² Determine if…

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Q: f(3x² − 4x+6) dx ; y = 10 if x = 1. Solve for the constant of integration. Given

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

Q: A street light is mounted at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the…

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Q: Let r(t) = (2t5 + 4, − 5e-4t - 3 sin( – 5t)). - " 1 fr(t)dt (don't include the +C) Find fr(t)dt = (…

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Q: eft co Evaluate cos² (9x) dx.

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Q: Use the Product Rule or the Quotient Rule to find the derivative of the functic y = 7x5 sec(x) y' =…

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Q: 4 3 + kxy¹ − 2x)dx + (3xy² - 20x²y3³)dy = 0

A: Topic:- differential equation

Q: Find the point at which the line r(t) = ( − 6, 3, − 3) + t(6, 5, — 5) intersects the xz - plane.

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Q: Using the squeeze theorem, evaluate: lim v2 + cos(v) v--> -∞ 5 + v -…

A: Apply squeeze theorem to evalute  limv→-∞v2+cosv5+v-2v2

Q: f'(2). f(x) = f* (2t - 3) dt

A: Topic:- application of derivatives and integration

Q: Find the transform of the given function by use of a table. f(t) = 3e-4t sin 5t A B C D E F (s) =…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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

Q: 3. Let R be the region bounded by the graph of y = 1-² and by the positive coordinate axes. Using…

A: Volume of a solid form by cylindrical shell method is given by V=∫ab2πr(x)f(x)dx     where,   a≤x≤b

Q: 9. Find the vertical and horizontal asymptotes of the following functions. (a) f(x) = 9x² - 4 2x2 X…

A: a) f(x)= (9x2-4)/(2x2-x) b) f(x)= (x2-3x4)/(x-1).

Q: 8.5.39) 81 √x³1-qxz dx 81 __81 A+B. ८ (x) 7xx *(x - १) X X X 7

A: We can solve this above given indefinite integral by partial fraction method.

Q: Let F(x) = f(x³) and G(x) = (f(x))³. You also know that a² = 10, f(a) = 2, f'(a) = 8, ƒ' (a³) = 6…

A: Given that Fx=fx3 and Gx=fx3 The given values a2=10, fa=2, f'a=8, f'a3=6 We have to find the values…

Q: Let a and b be real numbers. Consider the function y = f(x) = 1x² ax+b For which values of a and b,…

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Q: Find all critical numbers of the function ƒ(x) = sin²6x + cos6x¸ 0 < x < / Select one: a. b. C. O d.…

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Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

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Q: Consider the space curve (t) = (6 cos(5t), 8 cos(5t), 10 sin(5t)). a. Find the arc length function…

A: As per our guide line if multiple questions are posted we are supposed to answer only the first one.…

Q: Yall are starting to waste a ton of my time with these wrong answers.

A: For y=1x2, to use differentials to approximate  the change in y when x changes from 4 to 4.125.

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

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Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point. f…

A: we need to find out the function whose derivative is given.

Q: Find the vector component of v = 2i - j + 3k along b = i + 2j + 2k and the vector component of v…

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Q: Find the equation of the line through Po = (-2, 1, 1) and parallel to the line r(t) = (2, -2, 3) +…

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Q: Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify…

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Q: Find the value of the derivative (if it exists) of f(x) = (x+3)³ at the indicated extremum. Select…

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Q: Evaluate the definite integral. 2 2 sec-¹(x) 2 x √ x ². 1 dx

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Q: limx -> 2 (x2/(x-2)2)

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Q: Write an equation of a line tangent to the graph 3x² = -3y² + 75 at the point (-4,-3).

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Q: Find the horizontal asymptote, if any, of the graph of the rational function. 16x 2 8x²² +3 f(x) =…

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Q: Find all the critical numbers of y=x²-2x²-3, then determine the local minimum and maximum points by…

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Q: Find the following derivatives. Express your answer in terms of the independent variables. 3x - 3z…

A: The objective of the question is determine the partial derivative of the given function.

Q: S 0 ecos sin 20 de

A: Topic - Definite integral we are given ∫0πecos θsin 2θ dθand we know that∫exdx=ex+Cand integration…

Q: Let y = 8x² 25x Find the differential, dy. Ody=16xe 25x+200x²25x Ody=400xe 25x dx dy=(16xe…

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Q: 1 ¹/ de by first rewriting the denominator as a single trigonometric function. cos + sin 0 3. Find

A: We need to find out the integration.

Q: Find the linear approximation of f(x)=√x when x = 81. 1 108 O L(x)=3+ -(x-81) OL(x)=81+ 1 108…

A: We have given function  fx=x4 Put x=81 f81=814=344=3 Linear approximation at x=a is given as…

Q: The region between the graphs of y = ² and y = 3r is rotated around the line = 3. The volume of the…

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Q: Find the distance (d) from the point (- 6, 1, 0) to the plane - x - 2y + 5z = d = - 49. I

A: See this solution in below.

Q: sec(log3 m) dm mln 3

A: ∫seclog3mm ln3dm

Q: Match the following to create correct hyperbolic function identities and inverse hyperbolic function…

A: From the given identities, we have to match the correct values. Note:   Multiple questions are given…

Q: Compute the values of dydy and ΔyΔy for the function y=e3x+2x given x=0 and Δx=dx=0.02   Round…

A: Given,y = e3x + 2xDifferentiate 'y' with respect to 'x' we get:dydx = 3.e3x + 2dy = (3.e3x +…

Q: 14. Find the value of the constants (a, b, or c) that makes the following functions continuous: if x…

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Q: Find the value o the derivative (if it exists) of the function f(x)= x² x² +9 -8 -6 -14 Select one:…

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Q: Find the point at which the line r(t) = (6, − 8, 1) + t(4, 7, − 2) intersects the yz plane. -

A: Here we have to find the point of intersection

Q: Assume that f and g are both differentiable functions. Find h'(0) if h(x) = ³√f(x)g(x), f(0) =…

A: See this solution in below.

Q: lentify the equation as a homogeneous or exact equation differential equation. then solve the…

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Q: the follwing initial value problem. Solve the Write your answer symbolic aly. Include No decimals in…

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Q: Differentiate the function: y=15 y′=

A: Given, y=15

Q: П Let a = ci + j and b = 3i + 4j. Find c so that the angle between a and b is 6 Round your answers…

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