Show by change of variables that T(x) = 2 -L +2x-1e-1² dt = -xF e du.

Q: Suppose that x and y are related by the equation Proportionality 1 dt. Vi + 4t² |Show that d²yldx²…

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Q: d_(F(x*)) d dt dx dx 16

A: To find- solve the given equation.

Q: Find F′(x).

A: Given Data The integral function is F(x)=ꭍxx+2(4t+1)dt.   Solve the given integral function,

Q: Solve for y: O y = Oy = x = 4ln(y - 8). 1 4 ln(x - 8) x+8 4 O y = e-4x + 8 O y = 4 ln(x - 8) Oy =…

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Q: i(t) = (A₂ + A₁t)e-at

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Q: Find  f ′(a)  f(x) = 2x4,    a = −1

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Q: The function y = 2x2 - ln 4x (x 7 0) has one minimum point. Find its first coordinate.

A: Given  y = 2x2 - ln 4x

Q: Suppose that a pdf for a continuous random variable Y takes the form ayya-1 y > 0 f(V) = (1+ yª)r+1…

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Q: 2. で-5e dt = 4.

A: ∫xndx = xn+1n+1

Q: Find the instantaneous rate of change of f(x) = 2x² - 8x + O 16 O -8 -16 O-14 8x+1 when x = -4.

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Q: d) S t3 – 2t2 – 1 dt t2

A: (d) We need to evaluate the following integral ∫13t3-2t2-1t2dt

Q: The probability distribution table describes Rhonda's movie collection. What is the probability that…

A: Here the given probability distribution table is :-XThriller DramaComedyAction science fiction…

Q: If a function y = f(x) satisfies = y, %3D then %3D dr y = e".

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Q: g(x) g'(5) = 2 X 13 1+t2 dt

A: Given query is to find indicated derivative.

Q: dx Find F(x) = S 1-2x+ 2x2

A: Here we solve the integration problem.

Q: dM/dt=4M, M=25000 when t=2   dT/dx=-3.2T-1328, T=-212 when x=2

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Q: dž 3 9. with x(0) = dt -1 -3 x1(t) = help (formulas) x2(t) : help (formulas)

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Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: 4. F(x) = (1- t) dt %3D 4

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Q: Determine the value of x for which f(x) = x³9x² + 5x-e7 +11″ has the lowest instantaneous rate of…

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Q: Normalize (z) = 3f2(x) +2f3(x). You can think of functions being 0 beyond the [0, L] interval, where…

A: Simple Linear Scaling:If f2(x) and f3(x) are linear functions that map the [0, L] interval to [a, b]…

Q: Find the relative rate of change if f(x)= 10 – 3e-4. %3D |

A: Given,           The relative rate of change of f(x)=10-3e-4xWe know that that,         The relative…

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…