r3 V9-x² »6-x-y dz dy dx in the order dz dx dy 0,

Q: siny dy 2. 3 |- cosy

A:

Q: Ssin" x 14 x cos' x dx Integrate:

A: Given,        ∫sin14xcos5xdx

Q: integral. et dx e2x + 3

A:

Q: et-x+l 2x –1 -dx by using substitution method. Integrate

A: First I have made a substitution and integral become easy and then solved . I have written all…

Q: ntial equation dy 1 x>0 + 2y = 1- dx

A:

Q: ind dy/dx of y= tan^-1 (ln x^2

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Q: tan20 sec2ede In 2 edx 3. 1. (a² + a²tan²0)² 2ex- 1 x'dx dx x- 1 2. 4. (1+ x2)3

A: As per our policy, only the first three subdivisions will be solved. For the remaining subdivision,…

Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

A:

Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: integral from 0 to 2 if (x^2 dx) / (x^2 + 4)^2

A:

Q: Integrate Jo tan h x dx

A: Use substitution method for integrate

Q: Using figualve mme thod X + 2 dt 2. dy X - 29

A: To find the eigenvalues λ of the matrix A, solve the characteristic equation A-λI=0 for λ. To obtain…

Q: itegral 6ze dy dx dz

A:

Q: = vt – 2, d²y t – 2. d²y y = t² – 3' dx2

A: x=t-2y=t2-3

Q: Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

A:

Q: integral arctan (1/x)dx

A:

Q: dy tanx Find dx for y = 1-secz %3D O 1 1) dy (1+secx)secx-secxtan'x dx %3D (1-secx) 2) dy…

A:

Q: integral from -5 to 4 of absolute x^2-4 dx

A: ∫-54x2-4 dx

Q: Differentiate. y =x° In x- dy II

A:

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: Find dy/dx by implicit differentiation. (1/x^3) + (1/y^3) = 4 dy/dx =

A: Given function (1/x^3) + (1/y^3) = 4  We need to find dy/dx using  implicit differentiation

Q: In 2x dx 3.

A: We have to find solution

Q: integral of sec^3 x

A:

Q: dy 1- cosh x + (sinh x)y = e¯x dx 2 dy 2- - y = e*/2y³ dx

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Q: (12z – 12z2 + 71z – 77 Integrate: 4x2 + 25 - la( |42° + 25|) – arctan X + C

A:

Q: Integral of dx/√8x-x^2

A: Given,            Integral of dx/8x-x2

Q: Find dy/dx 1. y = x^2(sin^−1 x)^3 2. y = e^tanh x/x^2 − sechx 3. y = tan^−1 (sechx) + sech(tan^−1…

A: We expert are following guidelines.We are supposed to do first question. We have to find dy/dx

Q: (b) YOUR TURN 4 Find dx. Vx f(x) deriv for in

A:

Q: integral from 2 to 3 of (x^3 - 2x) dx / x-1

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Q: 5.Differentiate.   y=3/2−4x

A: We will differentiate using chain rule of differentiation.

Q: Integrate Jxsin(x*)dx x sin(x)dx

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Q: (3 sin y – 5x)dx + 2x² cot y dy = 0

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Q: dy tanx for y = dx 1-secx 1) dy (1-secx)sec x+secxtan2x dx (1-secx) 2) dy (1-s8cx)secx-secxtan²x I3I

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Q: y= sinh-lx then prove that Vx2+1 dx

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Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

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Q: 2Linear edluotion 5. dy dx

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 3. f sin³y(2-3cosy)² dy

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Q: dy dx 118 (x = 3x - 5

A: Topic:- differential equations

Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

A:

Q: (siny - ysinx) dx +(cosx +xcosy) dy =0

A: We will use the method of exact differential equations.

Q: ntegrate dx/sqrt(E-((kx^2)/2)) ;    E,k = const.

A:

Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: 2olue dy %3D

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Q: integral of (2y-3x)dy and integral of (2x-3y)dx

A: We have to find the integrals of (2y-3x)dy and (2x-3y)dx seperately. Recall that the integration of…

Q: {dy}/{dx} for y=4sin^{-1}(x^2)

A: The explanation of answer as follows

Q: dy Use implicit differentiation to find dx X+3 %3D У -3 3y = dy %3D dx

A:

Q: Svaluate x dx from the definition of RS-integral.

A:

Q: Find

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.