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Q: Solve the differential equation with the appropriate method. Finalize answer equated to ky^n.…

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Q: This subject is DIFFERENTIAL EQUATION. SOLVE THE FOLLOWING APPLICATION PROBLEMS 2. The population of…

A: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: sin 2x (1 - 2 cos 2x)? dx 6.

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Q: 2.Solve bernoulli (x ^ 2 + y ^ 2) * dx - xydy = 0

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Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

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Q: Solve the given initial-value problems. 4.43. re dr +(y-)dy 0; y(0) 0

A: x ex2 dx + (y5-1) dy =0x ex2 dx =(1-y5) dyvariable separable;∫ x ex2 dx=∫ (1-y5) dyx2=tx dx =dt212∫…

Q: 3m 5. rad 9. 1.1 rad 13. 1.6 rad 4 6. rad 10. 3.1 rad 14. 2.1 rad 2- rad 3 11. 0.50 rad 15. 0.091…

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Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: 7y" - 18y %D

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y2, (6,…

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Q: Find the area bounded by the parabolas y^2 = 4 –x and y^2 = 4 – 4x.

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

Q: Which of the following is not equivalent to tan"? 2 1- cos 0 csc 0 + cot 0 sin 8 O Option 1 O Option…

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: To find the parametric equation of a line that passes through (-1, 4, -6) and is parallel to given…

Q: f(b) – f(a) Find the value(s) of c that satisfy the equation = f'(c) in the conclusion of the mean…

A: We can find the value of c that satisfy the equation  f(b)-f(a)b-a = f'(c) .

Q: integral. Give your answers as fractions 3 (i) dx V1- x2

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Q: Find 4小1 机g:f el fof (メ= 区 x = 3x # S 3. f位)EX

A: We have to find the fog gof and fof functions.

Q: Find all solutions of the equation. 3tan? (0) – 1 = 0

A: The given question can be solved as shown in step2.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: 2. y = loga(x³ + 2x – 2) 3. y = In³ (x + sin x) %3D 4. y = tan¬1(3x)

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Find an equation of the plane with the given characteristics. The plane contains the y-axis and…

A: Plane in 3D: The equation of a plane in 3D is ax+by+cz=d If by is removed, the graph of the…

Q: 3. * Sx² e** dx 1. pAx (8x? + 4х 1)+с C esx (8x? - 4х + 1) +С 16 16 1. 1. e** (8x2 + 4x - 1) + с 32…

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Q: 1. Determine whether the following integrals converge. (a) 1 dx x3

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Q: dy Find for the following expressions: dx a) y = x5 In(3x)

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Q: 1 Use the geometric series 1 >a* for |æ| < 1, to find a power series representation k=0 for the…

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Q: Find the general solution for the following equation: y''' + 3y'' – 4y' – 12y = 0

A: Solve the differential equation by assuming eλx for some constant λ.

Q: Integral Calculus: Integration by Parts (Original method

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Q: 1 1 dx

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Q: Question Select your answer. Find the value(s) of the constant k so that f(æ) = kx² – 5x + 1 and…

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Q: Evaluate by using homogeneous D.E. 3 (3x? + y²) dx – 2xydy = 0 O ao3 = C(9x³ + y³) O ap3 = C(9x² +…

A: ANSWER: OPTION 2nd

Q: Determine the maximum volume of a cylinder that can be inscribed in a sphere with radius of 10cm.…

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: Find f if f(x) = tanh (sin e*). -1 %3D e* Cos e* Cos e* 1- sin? e* | O Option 1 Option 2 e cos e* 1.…

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Q: y dy J 725 – 16y 2.

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Q: Given the hyperbola with the equation y – 9x? = -9, find the vertices, the foci, and the equations…

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Q: S sin 2x sin 4x dx 7.

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Q: Direction: Find the differential equation of the family of curves described. 4. Ellipse with center…

A: Equation of ellipse is x^2/a^2 + y^2/b^2 = 1

Q: 2pq If sin A = ,where A is an acute p2+q² • angle of a right triangle, what is sec A? p² + q? p² +…

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Q: Answer the following True or False. If f(x)dx 0 and f(x) is continuous, then a = b. O True O False

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Q: Question 12 V3 sin(0 + m) What are the solutions for the equation cos(o + 1) = 1,

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find k so that the following function is continuous on any interval. S f(x) = 7x 2 < x kx 0 < x < 2…

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Consider the following. u = -9i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find…

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Q: What is the approximate value of x in the figure below?* 723 58 427 3244 ft. 3169 ft. 820 ft. O 3322…

A: Find your answer below

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) = 4i +…

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Q: We use Law of Sines and Law of Cosines to solve for a triangle. When we say solve for a triangle, we…

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

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Q: dx V3+2x-x2 10.

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