Is the following force conservative? Why? F = - () e; - (), + () eo , where a, b and c are constants r sine

Q: Differentiate y = 7x+xtan x.

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Q: Use the properties of logarithms to expand the quantity.   log 10    sqrt (( x-1)/ (x+1))

A: The given quantity is, log10x-1x+1=log10x-1x+1=log10x-1x+112

Q: If w-f(a,b,c)=cos(ab)sin(b)+c, what is at -,6 )? 2 3

A: The given function is w=fa,b,c=cosabsinb+c and the point 12,π3,6. .

Q: Calculus Question

A: The function is not linear as it forms a curve when we increase the values of V, the value of I incr...

Q: Find the general solution of the differential equation (4 + tan2 x)y′ = sec2 x

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Q: Find the area of the parallelogram with vertices A(−4, 5), B(−2, 8), C(2, 6), and D(0, 3).

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Q: Use the graph of f(x) = x2 to graph g(x) = 2(x + 3)2 - 1.

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Q: Find all other zeros of p(x)=x3+6x2+21x+26, given that -2+3i is a zero.

A: Given Data The equation is p(x)=x3+6x2+21x+26.   Equate the equation p(x)=x3+6x2+21x+26 equal to zer...

Q: - 9x Let f(x) sin x + cos x f'(- T) =

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Q: Representing functions by power series Identify the functions represented by the following power ser...

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Q: Implicit differentiation Carry out the following steps.a. Use implicit differentiation to finddy/dx....

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Q: Evaluating integrals Evaluate the following integral. A sketch is helpful. ∫∫R y2 dA; R is bounded b...

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to fou...

A: ∫056sinxdx We need to use midpoint rule to approximate the given integral using n=4

Q: Evaluate the integral.

A: You can evaluate this integral using the substitution method. The substitution method is applied whe...

Q: Find the domain of the function : g(x) = √(7x-70)

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Q: Find the unit tangent vector to the curve 7(t) = (2 cos t)i + (5 sin t)j at t =

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Q: 11. . The table below gives values for functions f and g, and their derivatives. -1 3 1 2 3 3 1 2 -2...

A: Given

Q: Find the dimensions of a rectangle of maximum area having perimeter of 36 feet

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Q: Show that the rate of increase in the slope of the tangent at a point on the curve y = 2x3 is 12 tim...

A: Consider the given curve: Here the objective is to show that the rate of increase in the slope of t...

Q: (Sections 3.1 and 3.2) Use the method of triangular systems to solve the system of linear equations ...

A: Given system of linear equation:                                                 Ax = b where, b=-23...

Q: If lim

A: we have been given limx→c(f(x)+g(x))=3  , limx→c(f(x)-g(x))=-1find limx→cf(x)g(x).

Q: General (NO 115X A box is formed by cutting squares from the four comers of a 5"-wide by 7"-long she...

A: Authoring guidelines**** ---------------------------------------------------------------------------...

Q: Q13) the curvature of the circle of radius (r) is: * 1 O 4 Jua O 2 Ja O 1 Jua 3 J 2.

A: The position vector for a point moving on circle of radius r is given by: Rθ=rcosθi+rsinθj

Q: Question based on, "radioactive decay m(t)="..   I have tried it but still confused...   Any help wo...

A: Given Data: The function of remaining mass after t days is: mt=5e-0.088t   (a) At t=0, Substitute 0 ...

Q: 2a

A: Consider the given function,fx=x24-x+1,if0≤x≤535x-514,if5≤x≤10 First draw the graph for the values,

Q: 3. Find the vertical asymptotes of the function (x – 1)(x – 3)²(x + 1)? (x – 2)(x + 2)(x – 1)(x + 3)

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Q: The base radius of cylindrical vessel full of oil is  30 cm . oil is drawn at the rate of 27000cm3/m...

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Q: Advertising The effectiveness of a television commercial depends on how many times a viewer watches ...

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Q: Calc 3: Find a · b. a = 2j - 2kb = 5i + 3j + 7k

A: Given a→=2j^-2k^b→=5i^+3j^+7k^

Q: Determine the following indefinite integral. Check your work by differentiation.

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Q: The graph of f(x) = x* – 4x² is shown. Use this graph to sketch the graph of g(x) = |x* – 4x*|. -3 3...

A: Using the graph of fx=x4-4x2 we need to sketch the graph of  gx=x4-4x2  

Q: 1. A person's approximate brain weight is directly proportional to his or her body weight, and apers...

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Q: For the piecewise linear function, find (a) f(-4), (b) f(-2), (c) f(0), (d) f(3), and (e) f(4). 3x f...

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Q: PQ is  (-11, -15)  but you said (-11,15). So it is incorrect. Can you please work it again?

A: Solving only the part mentioned with the doubt as mentioned by the student. Plot the points P and Q ...

Q: Solve for the slope of the functions at the points specified using the limit definition of slope of ...

A: Consider the function  f(x) = 12x2− 9x + 15 point (−2, 81).  

Q: 1) Graph the function f by starting with the graph of y = x² and using transformations. f(x) =-(x – ...

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st ques...

Q: For which angle the equation |A·B = AxB is correct? 90° 60° 30° 45°

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Q: Differientiate the function. y=(2x-5)3(3-x4)4

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Q: Solve for all the red boxed parts

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st ques...

Q: Determine the value of the integral Integral sign: ((z^2 + r^2)^-3/2)x((2r)dr)

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Q: Use the piecewise-defined function to find the following values for f(x). 2-3x if xs1 f(x) = 4x if 1...

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Q: pleas show me the steps too, thank you!

A: Consider the given equations,x=t2-t,y=t3-3tFind derivative with respect to t.dydt=ddtt2-t=2t-1And,dx...

Q: The domain of a function f consists of the numbers −1, 0, 1, 2, and 3. The following table shows the...

A: Note that: x -1 0 1 2 3 f(x) 2 2 3 1 0 means f(-1)=2 , f(0)=2, f(1)=3 , f(2)=1 , f(3)=0   No...

Q: Q4) The vector product of two vectors is scalar product. F O T

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Q: Find all points on the graph of the function such that the curvature is zero. (0 <x<T) y = 8 cos x (...

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Q: Let s(t) = 4t + 24ť² – 60t be the equation of motion for a particle. Find a function for the velocit...

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Q: For a vibrating string, the rate of vibrations is directly proportional to the square root of the te...

A: Let v be the vibrations and t be the tension of the string. a). Given that the rate of vibrations is...

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.