Find div F and curl F if F(x, y, z) = x¹i − 6j + yzk. - div F= 7x + y curl F zi X

Q: Q4) A- Graph the following functions and determine (domain, range): (1) y=sin/x/ (2) y=/x²-2/ (1) y…

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Q: Question 9 of 20 View Policies Show Attempt History Your Answer Correct Answer Correct. Solve the…

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Q: Which of the following functions are solutions of the differential equation y - 3y = 6 ? 0 O y = -2…

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Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: Find the area of the inner loop of the limacon given by r = 1+2sin 0.

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Q: Determine whether the series Σ=1 (Limit Comparison Test) 2n²+3n √5+n5 converges or diverges.

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Q: Evaluate the surface integral s G(r) dA, G(r) = x+y+z, S: z=2x-y, 0 ≤ y ≤ 1, 0 ≤ x ≤ y

A: Given:    Gr=x+y+z,    S: z=2x-y       0≤y≤1, 0≤x≤y Substitute z=2x-y in Gr     Gr=x+y+2x-y…

Q: 35. Choose the integral which represents the area between two curves given on the picture. 2- 1…

A: To choose the integral which represents the area between two curves given on the picture.

Q: 1. Calculate the following unknown quantities. (a) P= (kx 1000), r= 1.2%, t= Find S.

A: As per the rules we can answer only first question and rest can be reposted.

Q: Find the conservative vector field for the potential function h(x,y,z) = 16xy ln(x+y) by finding its…

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Q: 6. Find the y" + y = sec³ x; y(0) = 1, y'(0) = 1. -√2 value (7) for a solution (x) to the initial…

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Q: Let y = 2√x. Find the change in y, Ay when x - 2 and Ax - 0.3

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Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

A: Here we have to solve the differential equation.

Q: A company manufactures mountain bikes. The research department produced the marginal cost function X…

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Q: Find the general solution to the linear differential equation: y" - y' - 2y = 0 O y = C₁e²x + С₂е¯x…

A: Given that a linear differential equation y''-y'-2y=0. We need to find the solution of this linear…

Q: D) lim f(x)=| 23 E) lim → 8 f(x) = F) lim f(x)= z 2

A: D) we know that, limx→3f(x)=limx→3+f(x)=limx→3-f(x)But limx→3+f(x)=2limx→3-f(x)=-1Since…

Q: S √√x+12 X S- dx using substitution. √√x+12 c. Verify that your answers to parts (a) and (b) are…

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Q: Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select…

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Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 2, t> 0

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) 200+600t 120t², where t is in…

A: The traffic flow rate across an intersection is rt=200+600t-120t2, where t is in hours and t=0 is 6…

Q: Evaluate 09 9121IN N OC 2 01 2 1 2 I -1²-2 dydx.

A: Given query is to find the value of the integral.

Q: 4. an = 6n 5. a = 6. 2n+2 a = (-2)n-2n

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Q: 1. Choose a solution to the differential equation y" - y = x²e² + 5.

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Q: Given: F(s) = (2s+3)/(s² -2s +5). Evaluate: f(1) Use 2 decimal places. 5.67

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Q: Hole with r=2 O 5 4

A: Let the lenght of the rectangular prism be=l        the width of the rectangular prism be=b and the…

Q: If N₂- My M equation = Q, where Q is a function of y only, then the differential M + Ny' = 0 has an…

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Q: For the function f(x) = 3x2 −x3 − 4 where −3 ≤ x ≤ 3, complete the following. 12. State the values…

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Q: Solve the initial value problem. ds dt I cost- sint, s = 3 2

A: To solve the initial value problem.

Q: Show the final answers using EXACT values only, not calculator-ba Show complete solutions. Evaluate…

A: solution given be;ow

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: For an arithmetic sequence, 017 = 47. If the common difference is 5, find: a1 = the sum of the first…

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Q: Let f be a function defined for t 2 0. Then the integral {f(t)} =[e-stf(t) dt is said to be the…

A: We need to find Laplace.

Q: Determine whether the equation is exact. If it is exact, find the solution. (e'siny + 3y)dx -…

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Q: (10 sin(x-sin(x-dx 6 2 (Ans: - sin(2x-2) + 5 x + C)

A: Given, ∫ 10sinx-π6sinx-π2dx

Q: Find the first three nonzero terms in the Maclaurin Series of f(x)=e^x sin x

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Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

Q: Find the curl of the function G = (xcosy)i + xy² j. (y² + xsiny) k ○ (y² + xsiny) î ○ (y² - xsiny) î…

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Q: Screenshot (168 Screenshot (168 Determine whether the differential equation (2x² − 2xy + 3) dx +…

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Q: 8] n=1 1 n√n +1

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x + 11 between x =…

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Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-tj² L{f(t)}…

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Q: How long will it take for an investment of $3,000 to double in value if the interest rate is 6.5%…

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Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 5 of…

A: Part(A): Apply the law of conservation of mass, which states that matter is neither created nor…

Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Find an equation for the conic that satisfies the given conditions. ellipse, center (-1, 3), vertex…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r = 4 cos 0 -…

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Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: Find F'(x). F (x) = 48 [아 dt t I F(x) =

A: To find out F'(x).