Consider F and C below. F(x, y, z)= yzi+xzj + (xy + 6z) k C is the line segment from (3, 0, -2) to (4, 4, 3) (a) Find a function f such that F = Vf. f(x, y, z)= • £² (b) Use part (a) to evaluate F. dr along the given curve C.

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Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

A: dPdt=kP1-PK Here K=carrying capacity ⇒K=5700 ⇒dPdt=kP1-P5700

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Q: 12 Evaluate the integral. 9 14 √(6x4-8) ¹4 9 dx

A: let  B=∫99(6x4-8)14dx

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A: To solve the following

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Q: (B) A different market survey shows that for every $0.20 reduction in the original $4 price, 10 more…

A: NOTE: Refresh your page if you can't see any equations. . a deli sells 480 sandwiches per day at a…

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A: .

Q: УА -3 -2 1 0 1 4 6 Т

A: According to question,given function,gx = ∫0xft dt

Q: Find f if f"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) = = 2e^t-3sint+ (2e^(pi) - 5)/(pi)t

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A: The solution is shown in step-2

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Q: Find the exact simplified solution to the equation below so that 0 ≤ t ≤. 1 + tan(t) sin(t) t = 0 X

A: tan (π - x) = - tan(x)

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A: Ratio of the number a:b:c  Then we consider the number are  ax,bx and cx

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Q: 15. lim ∞- - x → In (x + 1) x

A: We have to find the limit of:limx→-∞ lnx4+1x

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Q: The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand automobile tires…

A: given total profit P(x)=-x3+9x2+120x-400, x≥5

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A: The graph of g'(x) is:

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Q: 1. At what values of x does g have a local maximum? X Answer (separate by commas): x = 2. At what…

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Q: Find the domain of the given function f(x,y) = 3x² - 4y².

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Q: Does the series (-1)+15+1 n5 5+n4 n=1 converge absolutely, converge conditionally, or diverge?…

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Q: Determine the area that is bounded by the graphs of the following equations on the interval below.…

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Q: A company selling widgets has found that the number of items sold z depends upon the price at which…

A: Revenue, R = px

Q: 5. The graph shows the derivative, f'(x), of a function f(x). What do you know about f(x)? YA 8…

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Q: Verify the following identity. secsintan 0 = cos 0

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Q: c. Does the series converge or diverge? Σα 1 Clearly justify your conclusion. n

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Q: Graph the function, h(x) = 7 - 5*. -10 y +1+ 5 10 -10 -5 O -5 10 5 y -10 10 -10- 5 10

A: we have given equation for graph: h(x)=7-5x

Q: Solve the IVP: dy dt +0.4y = et, y(0) = 3.

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Q: Question: Determine whether the following lines are parallel, intersecting or skew. If they…

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Q: 48. lim xsin x x →0+

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A: Given: x     ifx&lt;11x    if x≥1 We are required to find: ∫-33f(x)dx

Q: Find the indefinite integral. Hint: Let v = eu + 6u. (Use C for the constant of integration.…

A: Indefinite integral

Q: Suppose that f(x, y) = x² - xy + y² - 3x + 3y with D = {(x, y) |0 ≤ y ≤ x ≤ 3}. 1. The critical…

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Q: If f(x) = then ƒ"(x)= = x S² (t³ + 4t 0 (t³ + 4t² + 6) dt SI

A: given,  f(x)=∫0x(t3+4t2+6)dtwe know→(i)  ∫xndx=xn+1n+1+c(ii)  d dx(xn)=nxn-1(iii)  d dx(constant)=0

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A: When drawn graph on Desmos graphing tool shown below  on [-4,4] by [0,20] F(x)=3^x G(x)=x⁴ so option…

Q: Find the exact value of the following expression. cos(60° +135°) O-1-√3 2√2 O 1+√3 2√/2 O 1-√3 2√/2…

A: let  H=cos(60°+135°)