Consider the following functions. f(x) 3 Vx - 3 g(x) = x – 3 %3D Sketch the region bounded by the graphs of the functions. y

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A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

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Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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A: we want to find the limit limx→0 ( cosx )1x2

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A: Given query is to find the area enclosed by the curve and x Axis.

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A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

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A: answer is in next step

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A: We can explain the answer in the following steps.

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A: To solve the given differential equation.

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A: The detailed solution is given below Thank you

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

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Q: The number of bacteria in a certain population increases according to a continuous exponential…

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Q: Consider the following. f(x) = x4 – 9x2 g(x) = x2 – 9 (a) Use a graphing utility to graph the region…

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Q: | (1– 2r)dr

A: Given:∫01(1-2x)dx = ∫011dx- ∫012xdx                     ∫fx±gxdx=∫fxdx±∫gxdx…

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

A: We can solve as follows