Find curl (4z i + 5x j+ 3y k).

Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 5 cos(9x – 10y)j+ 10zk. V·(V × F) =

A: topic- vector field

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Q: 24) use the Refio Test to determine tue canvergen ce or divergence of tue seri's 7n (~1)"(4)'…

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Q: The ODE below models a spring, mass, dashpot system with damping constant c, spring constant k and…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 9, f'(9) = 5…

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Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

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Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A: Let's find.

Q: dy -1

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Q: Disgraced my answers for step 2 or exercise b, plewse just answer all of the boxes; thank you!!

A: Please see the below picture for solution.

Q: Evaluate the definite integral. Use a graphing utility to verify your result. (8t – 1)2 dt 0.

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Q: 1. For the curve x2y2 = 25 at (-1,-5), find the equation of the normal line.

A: The given curve is: x2y2=25 Differentiating it with respect to x: y22x+x22ydydx=0 at (-1,-5):…

Q: Step 1 |an + 1 an + 1 n+ 1 1, or lim = 00, then n00 an Sa, diverges. For any fixed value of x such…

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Q: A mass attached to a vertical spring has position function given by 8(t) = 4 sin(4t) where t is…

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Q: Find y ify=xIn(9x+1) 2.

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: 6. The rate of growth of a particular population is given by dp 50t? - 100t3/2, where P is the…

A: Given problem:- The rate of growth of a particular population is given by (dp)/(dt) = 50t2 - 100t3/2…

Q: Setup the iterated integral using the order dydx and dxdy. Sketch R. // (Va+ e") dA where R= {(x, y)…

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Q: Indicate whether the given series converges or diverges. If it converges, find its sum. 00 cos kT…

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Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: Use L'Hospital to determine the following limit. Use exact values. In r lim glnz

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Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

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Q: Find the area of the shaded region. x = -y x = 2 – y? -2 2 10 В

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Q: Consider the system of differential equation x' = 5x – 3y - y' = 9x + 9y Write the system in matrix…

A: To find the matrix A.

Q: Radius and Interval of Convergence of a Power Series. 00 Determine the radius and interval of…

A: Solve the following

Q: Expand the binomial using the binomial theorem. Show all of your work. (z- 4) °

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Q: Problem 4. The third term of a geometric sequence is 9, and the common ratio is 2 Find the fifth…

A: Given :3rd tern of GP is 9common ratio=32

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F & curl F:

Q: V3x - 2 lim tan- %3D x + V3

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Q: (А) True B) False

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Q: Find the limit, If it exists. x- 1 lim X---

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Q: (c) Use de Moivre's formula to write down a formula for all o words, give a formula for the complex…

A: answer is in next step

Q: 6) Shared by the circles r = 2 and r = 4 sin 0

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Q: Problem 3. A stone is dropped in a lake, creating a circular ripple that travels outward at a speed…

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Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: Identify the function and interval which does not meet the conditions for applying the Mean Value…

A: We have to solve above question

Q: Suppose we have the position function: r (t) = t. t2 Evaluate the tangential component of…

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Q: Question 21 (-1 )dr In (z + a+ 1) + v3 sin In ( + + 1)-3 tan O 2 In(z +a + 1)-V3 sin () 2 lu(r i…

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Q: f(x) = x3 + x2 - 6x y 30- g(x) = 6x 20+ (3, 18) 10+ -10+ -20- (-4, -24) -30- 2.

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A: solution:-limx→1sinx-1x3+4x-5 ,  it is  00   formusing  L'Hospital's…

Q: 7. An analyst has found that Tom's Transmissions Company cost function is: C(x) = 40,000 + 500x –…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: 3 lim (1+ 4 x2

A: Given query is to find the limit of the expression m

Q: Which of the following differential equation has the same order and degree? [dy]6 + 5y = e* A. + 8…

A: See the answer below

Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: Determine using the giveti graph if the function f is contimuous on the following intervals: EXAMPLE…

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Q: For AABC, you are given mZC = 123°, mZB = 44°, a = 11ft. Find c. 40 ft 44.2 ft 41 ft 38 ft Previous

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Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

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Q: y = x and y = x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the…

A: We use circular ring method.