Find the smallest root of the equation f(x) = 2x – 6x + 11x – 7 = 0

Q: B1(b): Solve the initial value problem : f' (x) = x12 – 4x4 + 12x + 13 and f(0) = 2.

A: The given differential equation is f'x=x12-4x4+12x+13 and the initial condition is f0=2. Solve the…

Q: Approximate the value of the root of f(x)=-3x³+5x²+14x-16 near x=3 to within 0.05 of its actual…

A: Given : f(x)=-3x3+5x2+14x-16, to find the value of the root near x=3.

Q: Find the general solution of the equation x' + 5x(t) = 3.

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Q: show that the 2x2-y2=C is a solution to yy'-2x=0.

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Q: y" + y' - 3y = 4sin 2x

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Q: (x3-2x2+1)dx (x2-2x+5)2

A: Let I=∫x3-2x2+1x2-2x+52dxx3-2x2+1x2-2x+52=a1x+a0x2-2x+5+a3x+a2x2-2x+52Multiply equation by the…

Q: Find the number of units x that produces a maximum revenue R in the given equation. R = 108x2/3 −…

A: R=108x2/3-6x

Q: D. y" + y’ - 3y = 4sin 2x

A: This question is related to differential equations, We will solve it using given information.

Q: 3. Solve for the root(s) of the equation f(x)=3x³-4x²+8x+4

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Q: Solve f(2) for f(x) = -4x + 3 %3D f(2) = [? ]

A: Put x= 2 in equation We get  - 4(2) + 3 -8 + 3 - 5

Q: Find f by solving the initial-value problem. f'(x) = 7e* – 6x³, ƒ(0) = 5 -

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Q: Solve for x x'(t)=x-t

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Q: 2. Solve for x: (a) -3.x* +2=0 4x3 +5x3 – 6=0 4x +5x -6=0 (d)

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Q: Solve the initial value problem: f(x)-x7+12x+17 and f(0)=3.

A: We will rearrange and then integrate both sides to find the solution of the given initial value…

Q: Find a (real) general solution. y" + 2y' + 2y = 4e¯* sec³x

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Q: Find the general solution of (D3-D2+D-1)y = 15sin2x using method of undetermined coefficient.

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Q: solve for y in terms of t or x, as appropriate.

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Q: Solve * + 3x - 4x = 20t, given that at t = 0,x = 0 and i = 0.

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Q: Solve the fallowing: X+3Y=40+ 1 X-2Y=D9

A: Let's solve equations.

Q: Find the general solution of tx -3x = t³+2t for t> 0.

A: Given DE is  tx'-3x=t3+2t .......(1) We find the general solution of (1).

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: Find the general solution to x”-3x’+2x = e^t

A: First we find complementary function then particular integral and then general solution.

Q: of f (x) = 1³ + 2z² + 3x + 6?

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Q: fG)=4x-3 SCx) == (s09) (x)=

A: gx=x2

Q: Solve for f(2) f(x)=-3x+3 f(2)=?

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Q: Is function  y=x2 a solution for equation of (1-x3)y'-2x+x2y+y2=0? If it is, find the solution.

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Q: Solve (x + 2)x 4 geometrically by constructing a line segment of length x .

A: We can expand it by multiplying x inside bracket then it is parabola equation then draw the parabola…

Q: An equation for the stretched y = x2 -1 vertically by a factor of 3.

A: If we have a function f(x) vertically stretched by a factor of 3 function is g(x): g(x) = 3f(x)

Q: Solve the equation 2x² – 3y² = 6 for y. Is y a func- tion of x?

A: Given equation is 2x2-3y2=6. To solve for y and  to determine whether y is function of x. Solution:…

Q: Find f by solving the initial value problem. f '(x) = 9x2 − 12x, f(2) = 6

A: Given   f1(x) = 9x2-12c  f(2) = 6

Q: Show that the equation 2/x– 1– Vx = 3 has a solution.

A: Equation is 2x-1-x3=3

Q: Find the point(s) of intersection. f(x) = 2x2 − 7x − 18 and g(x) = 3x + 10

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Q: For the function z = x3 - 2x2y2 - 2y2 Please solve Zx and Zy

A: To find: The value of zx and zy. Given: The function is z=x3-2x2y2-2y2. Formula used: Power rule of…

Q: Solve for y in terms of x   7x+3y=2

A: We first subtract 7x from both sides    7x+3y=2 7x-7x+3y=2-7x 3y=2-7x

Q: (b) f(x)=2x +7atx =0

A: Answer

Q: Find the number of units X that produces a maximum revenue R in the given equation. R= 36x2/3 -2x

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Q: Solve for the general solution: y' – 5y = x³e*

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Q: .3 t +y3

A: Derivative is below

Q: Find the root of the equation x'-4x - 9 = 0 between 2 and 3 using the secant method & = 0

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Q: f(x) = 2x² + 8x at the point x = 2. %3D

A: Given data:     The given function is: f(x)=2x2+8x   The expression for the differentiation of the…

Q: Solve for x. Show all of your work. 10x + 10 11x + 2

A: We have to find the value of x

Q: Use variation of parameters to solve y'' - 7y' +10y= e^2x.

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Q: Solve f(x)=2x2+7x-4 and select all of the solutions below. C%3D X=-4

A: Given: f(x)=2x2+7x-4

Q: Solve for f(-1). f(x) = -3x + 3 %3D

A: The function is given as fx=-3x+3 The objective is to find the value of f(x) at f(-1)

Q: b) Approximate the value of the root of f(x)=-3x+5x+14x-16 near X3D3 to within 0.05 of its actual…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to calculate the root of the equation:…

Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…