The solution to the IVP, is x₁(t) x₂(t) x₁'= -3x1 - x2, x₂= 13x1 + 3x2, = = x₁(0) = 2 x2(0) = -8

Q: FX)=f(f(x))and G(x)= (F(x) F(4)=13f(13 )=3 f(13)=6f(4)=6 OF(4)- G'(4)=

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Q: In Z12, solve (a) x² = 1 (b) x³ - 2x²-3x = 0

A: In Z12 solution of  a) x2 = 1 b) x3 - 2x2 - 3x = 0

Q: S(x) =x-5x+1, -2 <x<3

A:

Q: If h(x) = x² + 2 then h*(11) + h(-4) is

A: We have to find the value

Q: r(x) = [(3x-2)/(2x)], find r '(x) O O [(3)(2x)-(3x-2)(2)]/2 O [(3)(2x)-(3x-2)(2)] / x²…

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Q: h(x) = 4(2x – 3)*(2x – 5)³ , find h'(x). Factor Fully.

A: Given query is to find the derivative of the expression.

Q: f(x)= 3x2 -2, find f '(-2) O -12 none of these answers O 12 6x

A: Consider the function  f(x)=3x2−2

Q: = Solvex (t) = Ax(t) where A 3 -2 [1] [8] = 4 and (0)

A:

Q: x+1 Find the slope of the tangent line to the graph of f (x)=; at a=0 2x + 1 A -1 B 1 C0 D None of…

A: fx=x+12x+1 Note:- As per the company's guidelines, we are supposed to solve the first question for…

Q: 1. y = 3x? – 2x4 - 3x3 + − − 2x + 1; y(4) - 8

A:

Q: Differentiate. y = In [(x + 4)(3x- 2)(5 – x)] d In (x+ 4)(3x – 2)(5- x))] = || dx

A: We have, It is known that the derivative of ln(ax) is, and derivative of the function of u.v form…

Q: Find the general solution of (x+ 1)² -2(x+1) 9-(x²+2x-1) y = (x+1)² e*, y₁ = (x + 1)e is a solution…

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Q: (7) (4x³-9x² + 7x + 3)ex. dx = A) e-*[4x³ + 3x² + 13x + 16] + C B) -e [4x³ + 3x² + 13x + 16] + C C)…

A: Given,   We need to find the integral.   (A) ∫(4x3-9x2+7x+3)e-xdx

Q: When you substitute y''p and yp into the equation, where does the: 4Ccos(2x) and -4Dsin(2x) come…

A:

Q: Find the general solution of the DEs 1- f"(x)= y"(x)=12x +6x-8

A: The given differential equation is a second order differential equation so we will first reduce its…

Q: Max Z = 3x1 +5xz+ 4x3 2x1 +3x2 + 0x3s8 3x1 +2x2 + 4x33s 15 Ox11 + 2xz + 5x3 10 X1, X2.x3 all 2 0.

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Q: 2) Find of y = क सम्माय 2) r*+1)(2x+3)

A: Simplify the given expression and take log on both sides.…

Q: (5, 2)

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Q: Find (4z² + 3z")dz -1

A: In this question, we need to find the integral of the given function.

Q: 13) h(x)= 4x – 2; Find h(x +2)

A:

Q: Find the antiderivative of (25x2+48x+15)/(x-1)(x+2)2

A: Antiderivative of a function f(x) is given by :…

Q: 5. In Z12, solve (a) x² = 1 (b) x³ – 2x² – 3x = 0 -

A:

Q: Show that (z3 z4) -1 = (z3-1. z4-1)

A: We prove the given statement by taking Z3=x3+iy3, and Z4=x4+iy4. After using the fact of…

Q: evaluate x2 -(xy-y) for x satisfying x/9 -7 = x/2 and satisfying -3y -5=4y+23

A: See the details solution in below

Q: Consider the following problem; max F(x1 ,X2) = x,x3 subject to 6x + 3x3 = 72

A: Solution is given below:

Q: Is (-2 , 2) a solution of y = 1/2x + 3 ?

A: The given equation is,

Q: 1) 2x+8y=20 y=2

A: 2x+8y=20..................1y=2.............................2

Q: Verify that y = + C2x + C3xlnx + 4x² is a solution of x³y"" + 2x²y" – xy' + y = 12x²

A: Given y = C1x+C2 x+C3 x lnx +4x2y' = -C1x2+C2+C3 lnx + C3+8xy'' = 2C1x3+C3x+8y''' = -6C1x4-C3x2

Q: if f = {(1, −3)} 1) find h(x)=f(−2x−3)+4 2) if k = {(3,5)}, find a and b for which k(x) = af(bx)

A: Given: f={(1,-3)}.   k={(3,5)}