Compute the length of the curve r(t) = (2t, In(t), t² ) over the interval1

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

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Q: (3) Compute f ds over the curve specified. (a) f(x, y, z) = 2²,r(t) = for 0 for 0 < t < 1

A: Consider the equation

Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…

A: Let f(x,y)= 2xy , x=t/ln2 and y= lns Here we have to find the equation of the tangent plane to…

Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

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Q: Find the function f if. Vf-(3a²y + y², a² + 2xy), Vf dr with and without the Fundamental Theorem of…

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Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

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Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: The function f(x, y) = x2 – y² at the point (0,0) is saddle point. صواب İbi

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

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Q: (2) Find a smooth curve a in GL(2, R) passing through the identity such that a'(0) 1 0 Justify your…

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Q: 3. Determine the linear approximation for Vx at x = 5. Use the linear approximation to approximate…

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Q: Find the linearization L(x, y) of the function f(x, y) at P0 Then find an upper bound for the…

A: We need to determine the linearization of the function: f(x, y)=xy2+ycosx-1 at P01, 2 over R:…

Q: Find the linearization L(x,y) of the function f(x,y) = e 3× cos (9y) at the points (0,0) and 0,

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Q: 6. Let f(r, y, z) = e=² cosh y + z ar ff at the point P in the direction of :

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Q: 11. Evaluate the line integral F dr where F (x,y) = xy'i+vi and the curve C is the shortest path…

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Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: 3. Let X(t) = t2W (t) – 2 f sW(s)ds, Is X(t) a martingale?

A: X(t)=t2W(t)-2∫0tsW(s)dsWe know that, X(t) is a martingale, if,EX(t+1)=X(t)

Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy +8 at Po(5,5). Then find an upper…

A: We have to find the linearization L(x, y) of the function f(x, y)  and then find an upper bound for…

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

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Q: 3 ) Express f(t) in terms of the unit step function u(t).

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Q: YouTrylt 2 Find the linear approximation of the function f(x,y) =In(x- 3y) (7,2) at and use it to…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

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Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: Q2// A :-Compute for the following at t=1 z= ze", z =t, y=t1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Find the work done by F over the curve in the direction of increasing t. F = 3xyi + 4yj - 2yzk r(t)…

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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: (6) Find the integral of the function piecewise linear path from (1,1) to (2,2) to (0,2). b) 22.3…

A: Given the function Fx,y=ey-x,e2x

Q: (a) x² + zsen xyz = 0

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Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: Q4: Find f for f(x,y,z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

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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: 13. Let F (x, y) = (1(²y²)x, af(x²y? , a(y²) Y) and suppose that C is a smooth curve parametrized…

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Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: B) Evaluate the line integral F-dr, where F (x, y) = x²y³i+ x°y°j and C is the curve r (t) = (t³ –…

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Q: Find the linearization L(x,y) of the function f(x,y) = e* cos (9y) at the points (0,0) and ...

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Q: Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the…

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Q: Find the work done by F over the curve in the direction of increasing t. F=xyi + 8j + 6xk; C: r(t) =…

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Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Find that F = 12x²yi + (4x + 8yz²)j + 8y² zk is conservative, and find a function f such that F =…

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Q: Find the work done by F over the curve C in the direction of increasing t,where F=-5 yi+5xj+8z°k and…

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Q: Ext find the anen of the ragion bounded on the leftby the Curve yx, on the right by the line y and…

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Q: x + Y f(x, y, z) = x sin + e*% – 1

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Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: According to the given information, it is required to use green’s theorem to evaluate the integral.

Q: Use the Quotient Rule to compute the following: t2 + 1 at t = -2 dt \ t2

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