Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units) and carries information only about direction.

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Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

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Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: For the slope field shown, which could be a family of anti-derivatives?

A: To determine which of the equation is a family of antiderivatives for the given slope field.

Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: Find the derivative dy/dx of the hyperbolic spiral r=aθ.

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Q: 3. Prove that the directional derivative of f(x, y) = y² + 2xy³ + x³y² at point (0.1) in the…

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Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

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Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

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Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Compute the derivative of g(x) = cos(t) dt-

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Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: show that the differential eguation is exact, then solre that method using 2 2 dy- x²-x+y? |

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Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: What is the derivative of f(x,y) y° at P = (3, 1) in the direction toward %3D Q = (4, –3)?

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Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

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Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: Calculate the derivative 12x d dx In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: follow next step

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: What is the derivative of h(x, y) = e"Y at (2, 3) in the direction at an angle of 7 from the…

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Q: The delivery of an antibiotic through an intravenous line (IV) may be modeled by the differential dm…

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Q: d rcos t sin(x²) dx dt

A: Given,            ddt∫1cos t sinx2 dx

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Q: Find the point of intersection of the tangent line to v=sin(2r) at y=0 and the line %3D x+2y=5.

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Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k. %3D dr dt

A: Given

Q: . Let y =sqrtx Find the differential dy

A: To find, y=x To find the differential dy.

Q: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: y' – ey : = sin x

A: In this question, we have given a differential equation y'-ey=sin(x) here, we need to check either…

Q: calculate the required derivative using the chain rule. z.ton"() -1 - tan u =Y Cose » yarsin@ az -?…

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Q: Find the directiona derivative of f (x, y) = In(e* – 4y at the point (0, 0) %3D - in the direction…

A: We have to solve

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: 2. Suppose that a particle is moving along the curve 4x2 + 16y? = 32. When it reaches the point (2,…

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Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: Find the derivative dy/dx of the Archimedean spiral.

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Q: Show that r = (sin t)i + (cos t)j + V3k has a constant length. And r(t) is orthogonal to it's…

A: Note: We are supposed to answer only one question. Kindly repost other questions as to the next…