How much work is done by a variable force F(x) = 7/x  N that moves an object along a straight line in the direction of F from x = 1 m to x = 6 m?

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A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

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A: The objective is to find F'(x).

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Q: #1 Calculate the derivative d/dt ∫sec(8x+96) dx=    sec(8t+96) [67,t] #2 On what interval is the…

A: (1) Calculate the derivative ddt∫67tsec8x+96dx (2) Find the interval in which the derivative is…

Q: Find the directional derivative of f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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Q: Find the rate of change f(x, y) = ln(6x² + 9y²) at (v2, /2) in the direction making a (positive)…

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: What is the directional derivative of f(x,y)= 2x²+3y² at the point (1,1) in the direction of v =i-j?…

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Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: Find the derivative of f (z) = (2° – 5z) (2² + 6z – 6). a va la sin (a) f' (포) 3DD Please explain,…

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Q: The directional derivative of f(x, y) = 2e* cos y at (0, ) in the direction of v = (-6, 8) is

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Q: What is the value of f (5) if f (t) sin (Ta) dt :? 1

A: Given, ∫1xfttdt = sinπxx   We have to find the value of f5

Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: 2. f(t) = -3t – 10

A: To find Laplace transform of given function we use the formula of Laplace transform.

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

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Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: What is the derivative of y = sin1 (x² + 2)? dy dr /1-(z²+2)² dy O dr 2x V1-(2²+2)² O dz V1+(x²+2)²…

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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: Find the direction in which the directional derivative of f(x, y) = x? + sin(xy) at the point (1,0)…

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Q: Find the total differential. 4x + y w = 2z - 8y |

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Q: Find the total differential. z = 6x1°y8 dz =

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Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: What is the directional derivative of the function f(x,y) = 2xy- 3y2 at point po= (5,5) in the…

A: Givenf(x,y)=2xy-3y2 ; p0=(5,5) ; u=4i+3jWe need to find directional derivative Duf(5,5)where…

Q: Find the total differential. 2x + y W = 5z - 4y

A: For a function of two or more independent variables, the total differential of the function is the…

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Find the differential of f(x,y)=sqrt(x^2+y^3) at the point (3,2). df = ? Then use the differential…

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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: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

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Q: Find the directional derivative of f(x,y) v = 3i – 4j. x² sin 2y at (1, 7/2) in the direction of |

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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: Show that the derivative of f(x) = 2/x+3 is J (4) = VI ob no using the definition of the derivative.…

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Q: Find the rate of change f(x, y) = In(2a² + 5y2) at (v2, v2) in the direction making a (positive)…

A: First we have to find the divergence of the given function.

Q: Find F (x). "sec(x) F(x) = In(4t) dt Je F '(x) = %3D

A: Consider the fundamental theorem for calculus 1 using the chain rule. If f(x) is a continuous…

Q: 2s+3 13. F(s) = s2–5

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Q: find the directional derivative of f (X, 4) = 3x² + 5y² at the poin t (1,-1) in the dccection of V…

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Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

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Q: Confirm the approximations by using the linear approximation at x = 0

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