Determine whether the vector field is conservative. If it is, find a potential function for the vector field. F(x, y) = 5y conservative with potential function f(x, y) = 6y O not conservative conservative with potential function f(x, y) = = -52 5y conservative with potential function f(x, y) = 5x5 y 6x5 conservative with potential function f(x, y) = y

Q: 14. Prove that AC B if and only if An BC= 0.

A: The objective is to prove the above question.

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A: Follow the procedure given below.

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A: We will solve the required.

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A: Follow the procedure given below.

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A: Given Sequence 28, 14, 7............

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A: ft=t,0≤t<70,t≥7

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A:

Q: 21. The complementary solution, ye, of the equation y" + 2y" + y = 10 is (a) Ye= C₁e + C₂e + C3 (b)…

A:

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A:

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A:

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A:

Q: Evaluate the following iterated integral. ["""_p²sin(e) dp de de O 1872 3 O 872 3 T O 1090 7 I T

A: Evaluate the given integral which is in the form of spherical coordinate.

Q: 2. Determining Taylor polynomials from given derivative values. Suppose g is a func- tion which has…

A: Let's find taylor series of function g.

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A: We have to find the angle

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A:

Q: gle. Round to the nearest tenth when necessary or to the neares minute as appropriate. مت A 22m 26°…

A: The triangle has the measures A=26°, B=51° and AB=22m

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A: Let's find volume of solid.

Q: 7. Use the Root Test to determine if the series converges or diverges. a. b. k=1 W k=1 2k

A: The given series, a) ∑k=1∞k+12kkb) ∑k=1∞kek

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A:

Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A:

Q: Q16 3⁰ 3t+2 a) 1 b) J dt dr cos² r√5 + tanz dt (3-5t)²

A: see below the answer and calculation

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A: Given the rate of change in the number of barrels, B ia proportional to 2,300,000 - B(t) Here 't' is…

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A:

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: PLEASE TELL ME WHICH SOLUTION IS CORRECT. THE ANSWER PROVIDED ISN'T SHOWN IN THE PICTURE

A:

Q: II) Given: • tan a = 2√6, a € [0, π] 3 •cos 3 = and sin 30 5 Find the numerical value of the…

A: given tanα=26,  α∈0,πsince tanα is positive and α∈0,π, so α lies in quadrant 1

Q: Solve the integral: (A) B D In (2x² + 3x −4) ³ (4x + 3) dx integral: Sela (2x² + 3x-4 E In (2x² +…

A:

Q: (x-4) dx 2 x²+x-6

A: We can evaluate the given integral by using the partial fraction method.

Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 5x, x = 2 and x =…

A:

Q: Find the derivative of the transcendental function. 6e* y' =

A:

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: We have to find  the volume of the solid that results when the shaded region is revolved about the…

Q: dx √e²x -9 A. 3 sec¹e* +C S B. 1 sec ¹ (= ² + c = c.₁ /sec²¹ e ² + C C. ex 0-¹ (+ ²) + C et с 3 D.…

A:

Q: If the number of sales is inversely proportional to the price of a product, write the differential…

A:

Q: A region bounded by f(y) = √√√y + 1, y = 1, y = 4, and x = 0 is shown below. Find the volume of the…

A:

Q: Find the area bounded by the curve and y+ 4 = 0 y=x²-3x 3X

A:

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: Find the derivative of the function y=√4-3x.

A:

Q: f(x) = 2 x-6x-7 8-2

A:

Q: -Consider the function defined by the base: Find dz ) Prove that дz +y əx дz ду = sin 2z z =…

A: Topic:- application of derivatives

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A:

Q: Find the volume of a pyramid with height 21 and rectangular base with dimensions 5 and 7 using…

A: Let h be the height of the pyramid, l and w be the length and width of the pyramid. Note that, if x…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A:

Q: T Sin ³ de 3 1-cose

A: I have stated the used formulas in the solution

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A: Evaluate the limit

Q: did

A:

Q: An object with an initial velocity of v(0) = 5 has an acceleration of a(t) = t² - 5. What is its…

A: Concept: The acceleration is given by the derivative of the velocity  That is a(t)=dv(t)dt Thus…

Q: fr. sin ax cos 3x dx

A:

Q: St Can the Fundamental Theorem of Calculus be used to find ○ No, f(x) = √²+ x²-9 ○ No, f(x) = √² dx…

A: Given fx=∫04x2-9x+3dx

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A:

Q: A region bounded by f(y) = y, y = 8, and x = 1 is shown below. Find the volume of the solid formed…

A: Given, f(y)=y3, y=8, x=1