III. Given: ,X(0)= 0 ,0st< 4] X'-2X = G(t) where : ,124 Solve for X(t) IV. Given: X'(t) + 2 Y(t) = - 1 X(t) – Y'(t) = 2t where, x(0) = y(0) = 0 %3D %3D Evaluate y

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A: Given : ∫02fxdx = 3 and ∫25fxdx = -9   To find : (a)∫05fxdx (b)∫52fxdx (c)∫33fxdx (d)∫25-8fxdx

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Q: y = e"(1 – y²), y(0) =

A: We will find out the required solution for given differential equation.

Q: If 12√x+9√y = 159, find y'(x) by implicit differentiation. V Find the exact value for y'(25) in…

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Q: 01:- Find the first order derivative of each of the following functions: (1+x)3 sec(x2) y = ex.sin2…

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Q: Find y' and y". y': y" = y = (²+ √x) ³

A: SOLUTION-

Q: Find x?dA where R = {(x, y) | 9æ² + 36y? < 324} Round your answer to four decimal places.

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Q: a) L{te3t – sint + cost} =? 1 =? b) L-'s-2)(s2+25-5)

A: a) We have to find ℒte3t-sint+cost

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

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A:

Q: 2х + 3, х oʻ Evaluate ,f(x)dx. . Given that f (x)

A: First break the interval of integration. Then open the mode. And integrate it..

Q: 2+ cosh r (r² + 4) Compute the derivative of y = In I - (r+ 1) Compute the derivative of f(x) =…

A:

Q: If 6√√x + 15√y = 177, find y'(x) by implicit differentiation. y'(x) = Y I Find the exact value for…

A: Given :The function is shown as To aim : The aim is to evaluate the function by derivative with…

Q: d steps for each problem

A: Here we have to find the derivative of  1) f(x)=e-x2 2) f(x)=ln(x3-5)2 3) f(x)=lnex

Q: For the function f(x) = 7x° – 5x + 2x + 7, find f''(x). Then find f''(0) and f"(5). f'"(x) = Select…

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Q: cy(1) = 4, y'′(1) = −2. y = x²y" +7xy +9y = xº,

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Q: (a) Find y' by implicit differentiation.(b) Solve the equation explicitly for and differentiate to…

A: Given: 9x2-y2=1 To Find : (a) y'             : (b) y' in terms of x. To check : (c) both the…

Q: 3. h(x) = 6ln(x) = 4√x + 10x² find the equation for h'(x). 8 = (S)111# notesup

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Q: An implicit relationship between x and y is given by the equation x² + y² - 20x - 16y + 64 = 0. This…

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Q: For the function f(x) = x' - x + 4, write Newton's formula as f(エn) lf'(xn). F(xn) = Xn for solving…

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Q: Which of the following functions satisfy the equation: f'(x) = f'(x)? O The answer can be found on…

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Q: 10) f(x) = x³ + 2 f"(x) = ?

A: Given query is to find the indicated inverse function.