Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo tan-¹ (2x) dy - (ry - 2+8²) dx, (x 4 where C is the cardiod r = 1 + sin 0.

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A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

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A: Here we will find the slope of given line,

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A: As we know that ∫xmdx=xm+1m+1+C see below the answer and calculation

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A: topic- arc length of a curve

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A: I am attaching image so that you understand each and every step.

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Q: dx 2. √ √x

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Q: 03/ A. For the following function f(x). Find: ji. iii. m=? 1-4X m -UX.=-u P(1,-1) f(x)=x-2x² The…

A: See this solution in below

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A: Given :Invest Amount=P=$5000Rate =r=2%=0.02Time =t=5 year

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Q: 3. Translation: (x,y) → (x-6, y + 4) 5 -5 -5 Y C B X D 5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: The objective of the question is determine sizes if possible and evaluate the values x,y and z.

Q: Given that 2 ≤ f(x) ≤ 4 for 4 ≤ x ≤ 5, estimate the value of 5 0³/ [ f(x)dx 5 [²₁ <5 f(x)dx

A: Given 2≤f(x)≤44≤x≤5To find range of∫45f(x)dx

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A: Solution : Given that integral is

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Q: 3. What is the distance between two points (3,-1) and (-2, - 5).

A: Solution:formula: Distance between two points x1,y1 and (x2,y2)                Distance =…

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A: Here we have to find the inverse function and then its domain and range.

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A: I am attaching image so that you understand each and every step.

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Q: The pH can be calculated using the equation pH = -log(H"), where H" is the hydronium ion…

A: We can find the hydronium ion concentration as below.

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Q: Find an equation of the tangent line to the curve y = 3 arccos (1,4 π). Select the correct answer.…

A: Find an equation of the tangent line to the curve y= 3cos-1(x/2) at the point (1,4π) .

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Q: No calculators. Find the exact length of the curve. y=2+2x³/2, 0≤x≤1

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Q: 1. Find the equation of the circle passing through the points (1, 5), (-2, 4), and (10,-2).

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A: To evaluate the given limit .

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Q: 01 √ √(x + y + -1 -1 (x+y+1)dxdy

A: This question is based on double integration.