5. (a) Find the real constants P, Q, R, for which 3 P Qx + R x2 – x + 1° x3 + 1 x + 1 | Show that V3 dx = In2 + T - 3 3 x3 + 1

Q: 2. Consider the PDE u; - t ux+tu=0 for - o <x< ∞ and 0 <t< ∞ with u (0, x) = sine x. Determine u (t,…

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Q: 4. Prove that the equation x + sin(x) = 1 has at least one solution in the interval |3D Va + 3 (0,…

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Q: The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cos 0 e = 3rk…

A: Take denominator of f is equal to zero.

Q: 5- for y = (x² + 1)5 dx a)10(x² + 1)5 b) 10x(x² + 1)* c) (x² + 1)* 6- Sin 2x is equal to: a) sin x…

A: Answer of the above questions are

Q: - Determine the largest interval in which the unique solution of (t – 3)y +tan t y =t, y(n) =0 is…

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Q: 27. f"(1) = 12 + sin 1 28. f"(t) 29. f'(x) = 1 + 3x, f(4) = 25 30. f'(x) = 5x- 3x? + 4, f(-1) = 2…

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Q: A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4…

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Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: Show that each of the functions on the left is a 3-parameter family of solutions of the DE on its…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: d²y Find the solution for cos(x) (1+ x²) – 2xy = with the conditions %3D dx2 1+x2 y(1) = -1, y(2) =…

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Q: 1. The loop of y = x '(4 - X) 2. y = 6x – x², y = x²– 2x 3. у %3D2х y? + 4x – 8 = 0 4. An arch of y…

A: As per the guidelines we can solve 1 problem only

Q: A homogeneous string is stretched and its ends are at x = 0 and x 1. Motion is started by displacing…

A: The boundary conditions are y(0,t) = y(l,t) = 0 and initial conditions are y(x,0) = μ0sinπxl and…

Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: 8 12. If y = then what is %? dx Vx+4' dy а. 4x(x + 4) dy С. dx = -4Vx + 8 %3D dx 3 dy b. dx -4(x +…

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Q: B- Find the solution to the equation = k satisfying the conditions at ax2 1-- 30 at x 0 for all…

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Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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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: 1 The value of S dx at x=0 is sinx+cosx C V7 (Inv2+1) +c Cn|vZ+ 1] +c ㅇ글미VZ+ 1| + c c -공in(V2+ 1) +…

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Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: 12) The solution of 2lnx-In(x+ 2)=In2 is a) 0 b) 1 c) {-1,4) d) 4 e) поп 13) sin( 2 csc"1(2)) = b) -…

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Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

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Q: he Solve the y)-Sy'(x)+8y(x)-4y(x)-xcos(x) equation y,0)-cos(x)+xsin(x)- 41 19 sin(x)+ cos(x)…

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Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: Solve the he equation F)-5y'x)+8y(x)-4y(x)-xcos(x) 41 19 41 19 sin(x)+ cos(x) -…

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: If z = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O…

A: Since you have posted multiple problems we will answer first problem for you for remaining problem…

Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

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Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 0<x<T (-1)"-1 f(x) = { 27-x COS nX n<x< 27

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Q: f(x) = |x|, −π<x< T 1-(-1)" a. f(x) = 2 Σ=1 sin nx n (-1)"+1 00 b. f(x) = 1 + ² =1 - 2 πT n² (-1)"-1…

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Q: 1 = cos t and f(0) = 4 f(0) + f(0+ 2T) + f(0+ 47) ? If f(t) = cos t what is the exact value of %3D 3…

A: ft=cos t and fθ=-14

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i 5 .5 и 3

A: The function is given by  fx, y = sin8x-5y The point is x, y = 5, 8 The unit vector is  u = 35i-45j…

Q: (2 - 3 sin 30 + y) dy- (9y cos 3p- p+1) do 0, y (0) = 2 Dy+4y-6y sin 3p+ q-20= 12 O y-y+9y cos 30- p…

A: We have to find

Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

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Q: 3. Jlgu * Solve the D. E. to the I. V. P. sinx(e + 1)x- cosx - 1, y(0) =0 In (1 + cos x) =I+e O…

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Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 5 sin 3x. q². - 00 0, u(x,0)…

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Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: f() = Sin - 2 <u< -/ (9) ○テkラ1- 一2 -1 2. b) f(x) = t ? An cos (NTTX) + E Bn SinntIk ニし Ao Ao = ー2 ー2…

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Q: 4 Find the mul hiplicity of the foll owing faunchons 3 2. a-9xt 30 L -4yx at x= 3 and x=2 3. 2. ) f-…

A: We will first check whether the given values are roots of function, then we will find the…

Q: 1. L(e** + e¬* + x²) S-4 s+1 s3 e3 2. L(sin 2x + e²x+3) : 2 + s2+4 s-2 Hint: e2x+3 = (e2x)(e³) %3D…

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Q: 1. Eliminate the parameter tgiven x = t – 3 sint and y = 2 + 3 cos t.

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: [6 Let f(x) = |r| be approximated by sN(x) = }a0+E (an COS (") + b, sin (7). %3D n=1 Determine the…

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Q: 24 Show that the solution of equation satisfying the condition O T-0, as t0 (1) T-0, for x-0 and x=a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.