t: It F is conservative, the integration may be F(x, y) = yi - xj (a) r₂(t) = ti + tj, ost≤1 (b) r₂(t) = ti + t²j, 0≤t≤ 1 (c) r₂(t) = ti + t³j, ost≤ 1

Q: Work Problem 2 [ Question 1 You must provide a clear and detailed solution. Given the region D in R2…

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Q: If f(x, y) = = Select one: O True O False x² + 2xy + y³ 2x + 2y 3y² + 2x '(x² + 2xy + y³)²¹ (x² +…

A: As we know the expression for ∇fx,y. ∇fx,y=i∂∂x+j∂∂yfx,y=∂fx,y∂xi+∂fx,y∂yj   Given: fx,y=1x2+2xy+y3

Q: Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2…

A: The answer is given below:

Q: Model the data using an exponential function f(x) = Abx. f(x) = = X f(x) 0: 1 2 300 90 27

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Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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Q: Obtain an exponential function in the form f(t) = Aet. HINT [See Example 5.] f(t) is the value after…

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Q: Find a closed form for the infinite arithmetic sequence given by the recurrence system:  x1 = -1,…

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Q: The directional derivative of f(x, y) = xe + 2y at point (2, 0) in the direction of the angle = is:…

A: Given that fx,y=xey+2y at the point 2,0 and θ=π3 find the directional derivative

Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: Question оо Select one: O 0 O None of them. 8 WIN s): Evaluate 02 2n³ lim n→∞ n³ + 3

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Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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Q: Let f(x, y) = 2x² + 3y2, then (2, 3) is not a critical point of f(x, y). Select one: True False

A: I have calculated the critical point of the given function

Q: 1- On donne: a- Résoudre l'équation: f(x) = 0 b- Trouver la dérivée : f'(x) c- Calculer: f(In 2) 1-…

A: Given data fx=e2x-3ex where,x∈R We need to solve part a,b,c

Q: Evaluate I = √³/ 1-2i 2 (2Z+3) dz Ans 17+191 along the path x=2t+²₂ y=4t²_t_2 F ostsi

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Q: A 240 ft tower is located on the side of a mountain that is inclined 19° to the horizontal. A guy…

A: We have to find length of guy wire. We can apply law of cosine to find this length.

Q: Simplify 8logg(64)

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Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: A particle is moving with the given data. Find the position of the particle. 12. a(t) = 3 cost - 2…

A: 12) a(t)=3cost-2sint, v(0)=4, s(0)=0 13) a(t)=a, v(0)=v0, s(0)=s0.

Q: The double integral ydxdy equals: Select one: OA. 84 OB. 52 OC. 44 O D. 56 O E. None of them

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Q: 1) A continuous-time signal x(t) is shown in the figure below. Sketch and label carefully each of…

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Q: Find f'(x) if f(x) = -7x5 +4√x. f'(x) =

A: To find derivative f'(x)

Q: Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = x²i + yj (a) Show that F is…

A:

Q: Find the volume of the region bounded by y = √x and y = x rotated about x = -4.

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Q: (b) Determine whether the alternating series converges or diverges by using the alternating series…

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Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

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Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: Lect one: True False

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Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: 2 -2 [ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy. We have Select one: True False

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Q: 1₂x (x + y) dA, where R is the region that lies to the right of the y-axis between the circles x² +…

A: We have to evaluate the integral.

Q: Q1) () points) a) Sketch the region of D = {(x,y) :-√√4-y≤x≤ ¹,0 ≤ y ≤ 4} b) Reverse the order of…

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Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

A: Suppose that f(x) (here f(n)=an) is a continuous ,  positive and decreasing function on the interval…

Q: The value of the integral Select one: a. 3 b. None of these d. / [1² 17/12 2y³ dx dy is

A: Evaluating the definite integral

Q: 1) Use reduction of order method with y₁ (x) = e³x to find a second solution y2 for the DE: y" - 9y…

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Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² - 2x³ + 3y² + 6xy. b. s]…

A: Extreme Points of Function f(x,y)=6x2-2x3+3y2+6xy

Q: Is the following statement true or flase? Select one: True False 5 2 1² 1²0 2 5 = √ √ ² x dx) ( √ ²…

A: The objective of the question is evaluate the double integral and choose the correct option.

Q: Use the Laplace transform to solve the given initial-value problem. y + 4yet, y(0) - 2 Step 1 To use…

A: By using the Laplace transform to solve the given initial‐value problem.y'+4y=e3t, y0=2

Q: c) Consider the series: 5-1+ 5 25 + .. i) Is the given series a geometric series? Explain. ii)…

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Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

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Q: If A = 1 -9 -9 -6 -4 and AB = 1 D -1 9 -3 -3 6 ww -6 ? a ? ? PP ?? 9 5 B-1 9 ∞ C 3-8 1 what is the…

A: We have to multiply the two matrices then find the value of a.

Q: Given the triangle not drawn to scale A = 16/ A 25 13 , find the measure of angle A using the Law of…

A: We can find the angle A using cosine rule as below.

Q: Let f(x, y) = 6 - x² + 2y²-5x - y. The point (,) is a saddle point of the function Select one: O…

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Q: A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The…

A: Given problem:- A farmer is building a fence to enclose a rectangular area consisting of two…

Q: Let f(x, y) = 3x² + 2y² − 2xy — 1. Find the local maximum and minimum values and saddle points of f,…

A: Double integral, Maxima minima

Q: Solve the problem. 18) A beverage company works out a demand function for its sale of soda and finds…

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Q: Long-Term Investments This exercise is based on the following table, which lists interest rates on…

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Q: Question 3. (a) (b 2 1 0 -1 Evaluate the determinant of the matrix -1 1 Use the Cramer's rule to…

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = - 1

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Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A: This is a basic integration formula