Find the work done by F(x, y) = (x, Y) over the curve r(t) = (e' cost, e' sin t) (x² + y?)3/2 from (1,0) to (e2", 0) both directly and using a potential function.

Q: 2x² Find F'(x) given that F(x) = S," cos (t2 + 2)dt

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Q: Find the derivative of y = arctan(1 + e²x). О 1 yl= 1+(1+e²)² О 1+e2x yl= ○ yl= 1+(1+e²x)² e2x 2…

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Q: Assume that F= (e^x−y)i+ (2y−x)j, C1 is curve from (0,1) to (2,5) along the graph of y=x^2+ 1, and…

A: Given , F=ex-yi^+ (2y-x)j^ C1 is a curve from (0,1) to (2,5) along the parabola y=x2+1 C2 is a line…

Q: Sketch a potential f(x) given the following graph of the first derivative f'(x). Explain you…

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Q: Given r"(t) = (e^t, sint, cost),  r(0) = (1, 0, 1),  r'(0) = (0, 2, 2),  solve for r(t).

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Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

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Q: Find f. f ''(t) = 9/ squareroot t,    f(4) = 31,    f '(4) = 12

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: Find y' for (ry)”/” – 64 at the point (4,4). (wy)³/2 C At (4, 4), g' DE

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Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(xe^y) .

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Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: Find r(t) when r'(t)=(te^-t^2)i-(e^-t)j+k and r(0)=1/2i-j+k.

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Q: The equation of the line tangent to the curve F (x) = S e dt at a = %3D V1- O y-V2 = (=- ) O %3D y -…

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Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: find y as a function of x if y'" + 81y' - = 0 where y(0) = 1, y'(0) = 81, y"(0) = 324

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Q: Find y' and y'' given x2 +xy +y2 =1

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