Find the wark done by the Foree Field FoK x>ye^> along the parabola X=y+1 from (bo) to (2,1).

Q: Sketch the Part of tthe slope Field of y'=L for X and y be tween -5 and 5. Then add to your sketch…

A: Slope field of y' =1/y

Q: Determine the divergence of vector field E = 3x²x + 2zŷ + x²z2 at (2, –4, 0).

A:

Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

A:

Q: 4. If div F >0 in a region enclosed by a small sphere, the outward flux of the field across the…

A: Given: Divergence F>0 is enclosed by a small sphere in a closed surface . The objective is to…

Q: @ Consider the Funetion y= sinx t cosx on [0,3T1/2], use EVT to ind ab soluute mox min. %3D

A:

Q: When is the vector field continuous?

A: given,       Continuous vector field .

Q: Find the total work done in moving particle in a free field given by F = 3xyi – 5zj + 10xk along the…

A: The total work done by a vector field, F→ moving a particle along the curve r→(t) is calculated…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in the…

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Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F 3D6xi+ 6уј+ 6z k;…

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Q: Show that the vector field F = ( -z, 0, x) is orthogonal to the position ----+ vector OP at each…

A: Given data: The vector field in the Cartesian co-ordinates is given by, F=-z i+x k.  Here, I and k…

Q: Find the line integral F.dr of the vector field F=ax k over a curve C defined by a C rectangle in…

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Q: Why does a two-dimensional vector field with zero divergence ona region have zero outward flux…

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Q: |Determine whe ther He Veetar Field Con ser vattive, iF it is Find Function For the veetor Field is…

A: Since, a vector field is defined by the function:-F⇀(x,y)=7yxi^ -x7y7j^ +0 k^ -(i)Our Aim is to…

Q: Find the divergence of the field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

A:

Q: 4. Find the flow of the velocity field F = V(xy²z³) along the line segment from (1,1,1) to (2,1,…

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Q: What does it mean if the divergence of a vector field is zerothroughout a region?

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Q: Explain the meaning behind the expression foF-dr, for a curve C and vector field F.

A: To explain: The meaning behind the expression ∫CFdr for a curve C and vector field F.

Q: Explain why a potential function for a conservative vector field is determined up to an additive…

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Q: Sketch a two-dimensional vector field that has zero divergenceeverywhere in the plane.

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Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…

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Q: The work done by a force field in a moving particle around a closed path is zero.

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Q: compute dr for the vector field where Cis the line segment from Co.o) to Cli3)

A: Given vector field is, F=1+x2,xy2  The objective is to compute ∫CF·dr, where C is the line segment…

Q: .) Find the work done by field F = (-y,-x) along curve C: counter clockwise along semicircle y = v4…

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Q: 6. Use the fundamental theorem of line integrals to evaluate 2x dr + 2y dy where C is the line…

A: Let's understand the Fundamental Theorem of Line Integrals:

Q: Given two circles centered at the origin, oriented counterclockwise, and any vector field F, then…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: Evaluate both sides for the field- rectangular parallelepiped X = 0 and 1 Y=0 and 2 and Z=0 and 3.…

A:

Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…

A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5

Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: Find the divergence of the field. F = (- 6x + 8y – 4z)i + (- 8x – 5y + 3z)j+ (x + 5y + 2z)k div F =

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Q: Therefore, div(curl G) = sin(y) – sin(y) + 8 = Since div(curl G) is different from 0, we conclude…

A: Given that:div(curl G)=siny-siny+8=

Q: Let W be the region between the sphere of radius 4 and the cube of side 1, both centered at the…

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Q: Express the field D = (x2 + y)-(xax + yay) in cylindrical components

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Q: Compute the flux of the vector field (x3, – xy³), - out of the rectangle with vertices (0,0), (3,0),…

A: Given: F=x3 ,-xy5with rectangle with vertices (0,0) , (3,0) , (3 ,2) , (0,2) To find flux of vector…

Q: The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In…

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Q: How much work is required to move an object in the vector field given as F = yi+3x j Along the lower…

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Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: Find the line integral of the field F = over the straight-line path from (1,1,1,) to (2,2,2).

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Q: Show that f is not Riemann integrable on [0,2].

A: This is a question of R-integration and measure theory.

Q: 4. Verify that the two integrals in the circulation form of Green's Theorem are equal along a circle…

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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.

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Q: 6. Show that the system with vector field -x + sin(y) F(x, y) : -y+ cos(x), admits no periodic…

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Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = 9 sin 9x cos 8y…

A:

Q: Evaluate the work done between point 1 and point 2 for the conservative field F. F = 8 sin 8x cos 5y…

A: We have to find work done.

Q: Given two circles centered at the origin, oriented counterclockwise, and any vector field F, then…

A:

Q: Since the divergence of an inverse-square field is zero, the flux of an inverse-square field across…

A: it is false as

Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.