Use the Divergence Theorem to find the flux of F(x, y, z) = z³ i –x³j+ y° k across the sphere x? + y? + z? = a? with outward orientation. i

Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: Describe the graph of the equation. r = 8 sin 5t i + 8 cos 5t j O Itis a circle of radius 8 in the…

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Q: 36. a6-72, a13 = 26

A: Student has specifically asked for the answer to the Question-36. Hence, solution to that problem is…

Q: Question 2 Suppose f(6) = - 5 and f'(6) 5. Find the following. = d + 3x dz ((7x². : + 5)ef (²)) at x…

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Q: Evaluate (2x - y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 5

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Q: (a) Put a pair of brackets on the left hand side to make these statements correct. 17-2 + 8-4- 11 -…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: ,2 -1 dx 2

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Q: Suppose that f(x, y) is differentiable at the point (3, 1) with f(3, 1) = 4, fx (3, 1) = 2, and fy…

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Q: Solve sin(x) = – 0.13 on 0 < x < 2 - There are two solutions, A and B, with A < B= A =

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Q: Find absolute maximum & absolute minimum f define on C0, 2]

A: maxima minima

Q: 6. For each integral, state which trigonometric substitution you would use to integrate by…

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Q: fadin a chive Decay Ihe radioghye Kroghope Curhan-f has 8 hak lHe of 599 yeaks. What iş Hi decay'…

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Q: The car you are interested in has 16 color options, 3 engine choices, and 6 entertainment system…

A: Given ,  The car you are interested in has 16 color options , 3 engine choices , and 6 entertainment…

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) dx x2 + 1

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Q: Consider the curve parameterized by x 3t2 3 and y 2t°. Find equations for all tangent lines to this…

A: Here we have to find the equation of tangent line.

Q: Find the area under the given curve. y = Vx +6, from x = 0 to x = 16 The area is (Simplify your…

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Q: Find f+ g, f- g, fg, and fig and their domains. F(x) = V15 - 2, g(x) = Vx+1 Find (F+ g)(x). Find the…

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Q: . Find an equation for the surface area of the rectangular box. =(x, y) dy = . If the surface area…

A: We will solve the surface area problem.

Q: A. (2x +x+3 dx

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Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

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Q: Find the centroid of the region bounded by the set of curves y = 2x? + 10 ,y = 4x + 16 ,x =-2,and x…

A: Given

Q: 1. Graph the system of inequalities 2х + у S 50 4х + 5y < 160 x 2 0, y 2 0

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Q: Find the volume of the shaded region when revolved about the indicated axis. ... 21 x = /7+ y 14 (А…

A: This question is based on application of integration .

Q: √x²√9 - x² dx

A: We will solve the integration,

Q: 10. Consider the system of equations X, - 2x, + 3x, = 1 2х, — Зх, — 2х, 3 3 X, - x, - 5x, = 2 a.…

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Q: In the integration of (csc 5t)(cot 5t) dt, what is the correct "u"? * cot 5t 5t csc 5t O (csc…

A: This question is based on indefinite integral.

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question

Q: The results of an experimental drug trial to treat chronic stultitia are listed below. Women with…

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Q: Let f(x) = (x – 3)(5x + 7). Find an equation for the tangent line to the graph of f at x = 2.…

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Q: Evaluate the integral of the following using Miscellaneous Substitution X Sdx 1+x 5.

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: Evaluate F. dr. F(x, y) = 7xi + 4yj C: r(t) = ti + V4 - tj, -1 sts

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Q: 4. Evaluate: lim (a² + e-*)(= cac r) エー→0+

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Q: Describe several types of line integrals and discuss how they are related.

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t= 0 T(0) : N(0) =

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Q: lim f(x) and lim f(x) both --3+ r-3-

A: We have to consider the given statement is true or false according to the given information

Q: Differentiate h(t) = 54ª %3D

A: Solution of given question is written in below steps.

Q: Evaluate the integral of the following using Miscellaneous Substitution dx 4. Sa

A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. dy

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Q: Q5. Which of these statements is False А. (а?)3 — а6 в. а?а? — а 5 2.3 a a2 С. a3 = a¬1 D. a + a' =…

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Q: (b) Given the demand function P = 120 – 3Q, fixed cost, FC of 50 and variable cost, VC of 5 per unit…

A: Find your answer below

Q: dy 1. Find for the following: - dr f. 4x² - 9y² = 36 g. -+-=1 X y ... h. 3x°y+2xy² = 4 i. (3 - 2x) =…

A: f.4x2-9y2=36Differentiate w.r.t.x4×2x-9×2ydydx=08x-18ydydx=08x=18ydydxDivide18y on both…

Q: full

A: We will find the double derivative.

Q: For the quadratic function f (x) = −2(x+1)2 +2, find the vertex, x−intercepts (if possible),…

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Q: 01r (a)lev 7) Find the area of the region bounded by the curves y= x² and y = x+ 2. Sketch the area,…

A: In this question we have to find the area of region bounded by the curve and line.

Q: 2x + 3 x 1

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Q: Q11. Which one of these expressions in words does not equal 1? A. The natural log, In of the natural…

A: To find the Expression in words does not equal to 1

Q: A 25-year-old woman burns 550t cal/hr while walking on her treadmill. How many calories are burned…

A: A 25 year old woman burns 550t cal/hr while walking on tradmill.