Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

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A: As per our guidelines we are supposed to answer?️ only 3 question. Kindly repost other question as…

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A: area under the curve

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A: Given query is to find the derivative of the expression.

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A: To determine the solution of the given differential equation.

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2r-4-x 2-2r 3 in Ir+1+3Inlx-3|+C +1-3hx-31 +C Option 1 Option 2 2 In Ix + 1-31nlx-31+ C 2 In Ix+ 1+3…

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A: When derivative of f is positive then f is Increasing and when f' is negative f is Decreasing

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Q: Evaluate (z° + 6) dæ (z³+6)® +c А. 18 (z³+6)° В. +c (x³+6)* 16 С. z18 + 2x15 + c

A: topic - indefinite integral

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A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: Find V· (F × G), if F(x, y, z) = 8xi+j+8yk and G(x, y, z) = xi+ yj – zk. V · (F × G)

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Q: x – 1 - V3x +1 lim Зх + 1 x→5 X – 5

A: Solution:

Q: 7. Consider the function f graphed below. 2 -4 4 -2

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Q: 24) Find the maximum rate of change of at the given point and the direction in which it occurs.

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A: Given query is to find the Indicated derivative.

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A: Vector

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

Q: y 3.0아 (1, e) 2.5 2.0아 y-e* 1.5 1.0 y = xe*2 0.5 -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: dy x+3y. dx 2x

A: First order differential equation :  Consider the first order differential equation…

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

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A: given function : f(x)=log3x and g(x)=2from figure it is clear that intersection of both curve is…

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Q: Calculate the definite integral by referring to the figure with the indicated areas. y f(x) dx Dd x…

A: Consider

Q: 2. Use the Divergence Theorem to compute ffs F. dS for F = (xy, yz, x² z + z² ) and S the boundary…

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Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

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