5. * 1 dx х (In x)3 1 + C 2 (In x)² 1 + C 3 (In x)2 A C 1 + C 2 (In x)? B D z+C 3 (In x) O A В E None of the Above

Q: Consider the following planes. 3x + 2y - z = 42 x - 4y + 2z = 0 (a) Find the angle between the two…

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: We need to find orthogonal trajectory.

Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: Find the maxim um and minimu m value s of the the constraint x2 + y? + z? = 400. Maximum value is…

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Q: Solve the following items and show your solutions. a.) Find the general and particular solution of…

A: Let us consider a differential equation of the form, dx/dy +xf(y)= g(y) Then it's integrating…

Q: 24 = 0 oft?

A: To solve the given differential equation.

Q: Which of the following trigonometric expressions is NOT equivalent to 1? * csc? 0 – cot² 0 cos? 0 +…

A: To determine which of the given trigonometric expressions are not equal to one.

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

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Q: Is it log or ln that should be used?

A: You are right. There was a mistake from our end.  Here is the correct explanation: y=x3x Take ln on…

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: Direction: Solve the following equations using separation of variables. 4. sin(x)dx + ydy = 0, y(0)…

A: Given

Q: Fove that y = ln|| is a solution to 1+e-22 - xey-x² . Use the initial values x = 0 and y = 0.

A: Given query is to find the solution of the differential equation.

Q: Find dy and simplify whenever possible. dx sec x+tan x 1. у 3 sec x-tan x 2. у 3 е * соs e * — sin e…

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Q: 2. y = loga(x³ + 2x – 2)

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Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: Which of the following is not equivalent to cos(0 + 0)? cos 8 cos 0- sin 60 sin 0 1- 2 sin? 0 O…

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Q: Find dy for the following expressions: dx а) y = x5 In(3x) b) у %3D 2 cos + 2x3 3x2 + 7x + cos (x) y…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Direction: Find the differential equation of the family of curves described. 1. Find the…

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Q: 4. What is the geometric relationship between the two integrals below? et dx, In x dx Evaluate the…

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Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: 1) y= 3cos 4 +2 4 a: b: Period: d: Phase Shift: S C:

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Q: Consider the function f(x) = x2 - 9 (a) Find the domain of f. (Enter your answer using interval…

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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: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: A function f(x) passes through the points (15,24), (18,37), and (22,25). Use the Lagrange Formula to…

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Q: (0, о, 16), (12, 12, 0) (a) parametric equations (Enter your answer as a comma-separated list of…

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Q: The graph shown below is f(x) = 2x 2 - 1. If g(x) = Sốf(t)dt , find g '(3). %3D 4 2 X 54 3 -2 - V1 2…

A: g(x)=∫0xf(t)dtThenBy fundamental theorem of integral calculusg'(x)=ddx∫0xf(t)dt=f(x)g'(x)=2x2-1

Q: (x² + y) dx – xydy = 0 O 2y = x In cx2 O y? = x? In cx? O O

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Q: The value of p for the series En=1n! e¯n by using ratio test is 2 O 8.

A: Ratio Test: Let ∑n=1∞un be a given series such that limn→∞un+1un=ρ Then the series converges iff…

Q: Which of the following expressions represents the height of a right circular cone having a slant…

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Q: Solve the given initial-value problems. te dx +(y-1)dy=0; y(0) 0 4.43.

A: identify the differential equation and solve it.

Q: olve the differential equation with the appropriate method. Finalize answer free of fractions and…

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Q: Evaluate the following IMPROPER INTEGRALS. It is optional to double check your answers/solution for…

A: To evaluate the given integral.

Q: S (In x)²dx A x (In x)² + 2x In x + C C x (In x)² – 2x In x+ C в x (In x)² + 2x In x + 2x + C x (In…

A: Let,I=∫lnx2dxI=∫1*lnx2dxApply integraion by…

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: 10 (vi) / 1+ x dx x2 + 100

A: The given integral,     ∫0101+xx2+100dx

Q: 4) represent the jollowing angles an higono metric cirde a7. + K2n 3. 4. c7 t. Eld

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Q: 3 Given y = (1– V2x)°; Find dy/dx O dy :-3(1 – v22)? de O (E) None of the choices O dy 3(1 – V22)°…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: 3. y = ln³(x + sin x) 4. y = tan¬1(3x) cos 1 4x G ED DI 5. y =

A: All the questions are a solved below.

Q: e length and breadth of the floor of a room are 30 ft. and 20 ft. pectively. Square tiles of 2 ft.…

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Q: An ice cream cone is filled with ice cream and surmounted ice cream in the formof a hemisphere on…

A: Given problem:- An ice cream cone is filled with ice cream and surmounted ice cream in the form of a…

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

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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

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Q: S x³et*dx

A: A detailed solution is given below

Q: A cone was formed by rolling a thin sheet of metalin the form of a sector of a circle 72 cm in…

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Q: dy Find for the following expressions: dx a) y = x5 In(3x) b) y = 2 cos (+ 2x³ c) 3x2 + 7x + cos (x)…

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Q: y dy J 725 – 16y 2.

A: