3.8 If H = (x – y)a, + (x² + zy)a, + 5yz a, evaluate f H dl along the contour of Figure 3.28.

Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Assuming that the necessary derivatives of f(x, y, z) are defined, how are Dˆi f, Dˆj f, and Dkˆf…

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Q: he characteristic curves for the IVP u+4 u,+2 u 0; (x, 0) = sin x; - 00 C are O a. T= X-t . T=X- 8…

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Q: a)Fit a curve of the form 1 S(x) = Db-2.4 to the following data -0.5 3.5 5. 5 6.9 f(x) -1 2.5 8.3…

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Q: 10. Suppose that f and g are functions of x and y such that dg dy df af ag and dx dy and suppose…

A: The objective of the question is determine the functions f(x,y) & g(x,y) according to the given…

Q: Match the graphs A, B, and C shown with the functions ƒ(x), ƒ'(x), and integral

A: Given : The graphs of f(x) , f '(x) and Anti derivative of f(x)

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Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 23 + xe² =…

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Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

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Q: a² + y? – a*y³ f(r, y) x² + y?

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Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

Q: Suppose that f(0) = 1, f(0.5) = 2.5, f(1) = 2, and f(0.25) = f(0.75) = a. Using trapezoidal rule…

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Q: Suppose that f(0) = 1, f(0.5) = 2.5,f(1) = 2, and f(0.25) = f(0.75) = a. Using trapezoidal rule with…

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Q: Given F(2) = 1, F'(2) = 1, F(3) = 4, F'(3) find each of the following. (Enter dne for any derivative…

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Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: 4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's…

A: (a) Approximate f(x,y)=410-x2-5y2 at the point (1.97,1.02) (b) Check Euler Theorem for…

Q: 8. Find the value of a if F = (axy-z)i+(x+2 yz) j+(y - axz)k is irrotational. %3D

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Q: Find the linearization L(x) of the function at a. f(x) = rad(x),    a = 25

A: Given,

Q: 1. Consider the following function: y = f(x) = In (2r² + 6x + 5), for x > 0 (a) Calculate f'(0),…

A: Using Derivatives &amp; equation of tangent line.

Q: Find an equation of the tangent line y(x) of r(t) = (t',tº) at the point t = 1. (Use symbolic…

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Q: Consider the sinusoidal function y = f(x) shown below. 8 6. 2- 10 15 20 25 30 35 -2- -4-

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Q: Assuming that the following equations define z an implicit function of x, y and, z = f(x, y), for æ°…

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Q: 10 if the equations f(x, y, z)= 0, g(x, y, z)=0 can be solved for y and z as differentiable…

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Q: HW.8. Use farseval's theorem to find if f(t)=A e-alti Ans: A?

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Q: 1. (a) Let f(r,y)- cos(z + 2y). Compute the diectional derivative Df(r,9), where u- (b) Compute ff,…

A: Solve the following

Q: Find and simplify the indicated derivatives of the following funetions: (a) f(x, y,z) = (x+1)cos(x²…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 41. In Figure 4, which of graphs (A), (B), and (C) is not the graph of an antiderivative of y =…

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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: The graph of a differentiable function f on the ir [2,10] is shown. Find the trapezoidal approximat…

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Q: (3) (a) Find the local linear approximation of f(x) = /1+x at xo = 0. Use your approxima- tion…

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Q: Find the si0pe of the given Function メト at メ= y' 1.) u= Vler*) at x = 2) 4= In(3メ-2) a+ x= こ %3D

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Q: 3.5 Given that H = x'a, + ya,, evaluate H· dl, where L is along the curve y = x from %3D (0, 0) to…

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Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

Q: {x} € 1, Show that property (3) of a matroid implies: For any S e there exists y € S, such that S \…

A: Following is the definition of a matroid. A finite matroid M is a pair (E,?), where E is a finite…

Q: Suppose that the functions f and g, with linear approximations L, and Lz at x = a as shown below.…

A: Limit problem

Q: Suppose that the p.d.f. of X is as given f(x)=4x-1 for 0≤x≤1 and 0 otherwise Find the pdf of…

A: The probability distribution function of Y is:…

Q: , Consider the function f(x, y) = x'y + y – 27y. f has v at (3/3, 0). f has ? at (0,0). f has ? v at…

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: 14. If X has the PDF f(r) = 1/4, -1<r<3, zero elsewhere, find the PDF of Y %3D

A: Given,f(x)=14  ; -1&lt;x&lt;3Y=X2

Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 2³ + xe² =…

A: Given function z3+xez=2-y3+lny3 cos(y+1)

Q: 1.4 Using the graph in Figure 1.7 below, find Sº, f(t)dt and if the area of the shaded region is A,…

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Q: 36 – t2 dt. f(x) 4+ cos? (t)

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Q: 4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:…

A: prove of the above question is given below...

Q: 4. Assume that f (1,2) = 4 and f (x, y) is differentiable at (1,2) with fx (1,2) = 2 and fy (1,2) =…

A: Not:- We are entitled to solve only the first question, unless specified. (4) Concept Used: Linear…

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: Given F(x, y, z) = (tan y + cosh x Joi 2xy)i + (x sec² y - x² + 1)ĵ - 2zk, evaluate F. dR where C'…

A: Given that,  F→x,y,z=tany+coshx-2xyi^+xsec2y-x2+1j^-2zk^, Therefore, set fx=tany+coshx-2xy…