Consider the vector field. F(x, y, z) = (9ex sin(y), 2e sin(z), 4e² sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =

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A: This question is related to indefinite integration, we will solve it using given information.

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Q: 8. Graph the rational function. horizontal asymptotes. 3x-12 a. r(x)= x+1 Show clearly all x- and…

A: Graphs are to be drawn first and then asymptotes and intercepts need to be marked.

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Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: Solved below.

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Q: 11 Given ~ [²₁_f(x) dx = 0 and [ ² f(x) dx = 1 1 1 4 11 A 6 B C 0 55 0 evaluate • [²³f(x) dx - ²₁²…

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A: Topic:- application of integration

Q: Solve the int B ²+3x-4)³ (4x+3)dx integral: Seln (2x² + 3 eln(2x²+3x-4)³ + C (2x²+3x-4) (-4)³² (4x +…

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Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3

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Q: Estimate the slope of the line given to the right. Select the correct choice below and, if…

A: slope of line = (y2 -y1)/(x2 -x1 ) here y2 = 5 y1 = 0         x2 = 1    x1 = 0 slope = (5-0)/(1-0)…

Q: Find the area of the region bounded by x²y = 1, y = x and y = 4.

A: To find the area of the region bounded by x2y=1, y=x and x=4.

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Q: 10. Prove the identity: 2 + cot² (x) _ 1 = sin² x - csc² (x)

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A: Given problem:- Find parametric equations for the line tangent to the curve of intersection of the…

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Q: 3. Evaluate the integral: (1) (u-2)(+3) du @[²7/1 dx (3) rπ/3 cscxcotxdx

A: topic- definite integral

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Q: HW.1 X y 58 Find y. (10) for the following data in the below table. 6 9 14 17 10

A: We will use Lagrange's Interpolating polynomial to find y10.

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Q: tretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: To find the work done.

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A: To identify the family of curve.

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A: The given problem is solved below in detail.

Q: dx x²√x² + 1 2 18. 1

A: Use substitution method for solving this integral.

Q: (1) / 25 5 + 7x dx √x T/3 1+(cos0)² de (cos 0)² √3/³ 1 + (3) √x-4\dx

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