3. dy/dt = e e- -∞

Q: 1 lim- x+ In x 2 dt =? e

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Q: 9. dx dt = x2 – 5x + 4 =

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Q: 3. Find the derivative dy/dx of each implicit function in sub-items 3.1 and 3.2: 3.1. F(x, y) = x² +…

A: 1) F(x,y)=x2+y2+xy=0 2) F(x,y)=x3+x2y+y3=0

Q: et d Calculate dt \e +1) ()

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: (v) er-y de +e**"dy = o

A: We will solve the differential equation by the method of separation of variables.

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: 23. The graph of a differentiable function ƒ is shown. If h(x) = f(t) dt, which of the following is…

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Q: 1-Find the mixed partial derivative: w = e* +x In(y)+y ln(x)

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Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

A:

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: Expand d/dx (Yx)

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Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = ex at x…

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Q: y" - y' - 2y= e* %3D

A:

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

A: If Fx=∫π3xt2+1sintdt, then evaluate the value of F'x.

Q: dx? + (m – 1)(ax³ +b+ cy) = 0 dt2 How do you split this into 2 first order derivatives? Also what is…

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Q: t1 S[D] = [*ª dt D(t). By expressing D in terms of x and x = dx/dt, show that S[D] may be written…

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Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

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Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

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Q: 3.) dx + e dy = 0

A: The objective is to find the solution of the differential equation.

Q: 5. Let h(x) = 4f(x)- 59(x). Evaluate h'(8). 6. Let h(x) = f(x) Evaluate h'(3). %3D 2 g(x) 7. Find…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: (2xe" + e*)dx + (x² + 1)e'dy = 0

A: