1. Consider the two functions f (x) = cos 4x and g (x) = ) (a) Write down: (i) the minimum value of the function f (ii) the period of g (b) For the equation f (x) = g (x), find the number of solutions in the interval 0sxsn.

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

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Q: 17. 18. 19. dx/ (9x² + 4) sin³ x cos x dx (secs x) dx / csc x

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Q: Solve the equations in Exercises 1–16 by the method of undeterminedcoefficients. y'' - y' - 6y = e-x…

A: Solution:Giveny''-y'-6y = e-x -7 cos xFormula:(sin x)'=cos x(cos x)'=-sin x

Q: 1. Find the general solution of y'= cos²xcosy

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Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: on of period 2 pi in t. (x+sin r)(x

A: The differential equation is given as, dxdt=x+sin2tx-esint Let x=ft be the solution of the…

Q: Find the general solution of y'=cos²xcosy

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Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

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Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: 4. An electric current can be represented by the function y = 2 cos (27(x -0.02)), with time in a…

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Q: 4 f(0) = cos 0, 0s0s- %3D 3

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Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

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Q: iFind the general solution of the equation sin4x 19. Find the general solution of the equation cos2x…

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Q: y = e2* (c, cosx+ c, sin x)

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Q: The minimum value of cos x +3 sinx+ 5 is: - V10 А в 5 - 10 5+ V10 D 5 E -5 - v10

A: let fx=cosx+3sinx+5if we have to find minimum value of function then first derivative equal to zero…

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

A:

Q: The approximation of the solution x of the equation x In(x + 1)-x-2 0 accurate to within 10 using…

A:

Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

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Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

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Q: This problem deals with functions defined by f(x) =x + b sin x, where b is a positive constant and…

A: Given,   f(x)=x+b sin x  y=x+b :-Tangent to f(x)

Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

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Q: 3 f(x) = x° – cos(x) %3D х — - Solve this question by the Fixed-point method on the topic of…

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Q: 4. y = tan(x+ a), 5. y = Aex + Be2x, 6. y = A sin 3x + B cos 3x, ,where A and B are arbitrary…

A: According to bartleby guidelines when student ask multiple subpart question then expert must have to…

Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: (9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general…

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Q: find a linear homogenous constant coefficient equation with the given solution: y(x) =…

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Q: For the initial value problem: (1/csc x)y' +(cos x)y =-sin4 x, y(3π /2)=0 Compute the unique…

A: Answer

Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

A:

Q: 4. Solve the initial value problem (cosy)y' = sin²x cosx , y(0) = Give the solution implicitly. %3D…

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Q: Solve the initial value problem: f'(x)= cosx + sec2(x), f(pi/4)= 2 + ((√2)/2)

A: We have to solve the initial value problem where, f'x=cosx+sec2x and fπ4=2+22 Integrating both sides…

Q: If is a constant, differentiating a linear combination of cos wx and sinox with respect to x yields…

A: The given non homogeneous differential equation is y’’ + 6y’ + 13y = 18 cos x + 6 sin x     ……(1)…

Q: Determine the general solution of y' = cosx cos y

A: we have to find the general solution

Q: A mass weighing 32 pounds stretches a spring 2 feet. If the mass is initially released from a point…

A:

Q: 1. Use Newton-Raphson method to find sixth iteration of a real root of the equation: cosx-xe* =0…

A: Formula Used: xn+1 = xn - { f(xn) / f'(xn) } .

Q: Example B Consider the inhomogeneous equation Yk+1 – 2yk coS Ø + Yk-1 = Rx, sin ø # 0, %3D

A: Given           yk+1-2ykcosϕ+yk-1=Rk  ,  sinϕ ≠0       ... (1) where ϕ is constant and Rk is…

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* - 4e* Asinh x+B coshx…

A: Consider the following equation:…

Q: 2. f(x) = x – x + sin(x) – 1 Solve this question by the Fixed-point method on the topic of solution…

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Q: 1- LS7 cos(y)esin(y)+9x dydx 2

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Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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Q: (9) Verify that yp = sin 2x is a solution of y" – y = -5 sin 2x and use it to find the general…

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Q: The displacement x(t) cms at time t seconds, of a spring moving along a line is given by the…

A:

Q: A particular solution for y +2y +y=1-cosX

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

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Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.