0. The value 31 The function f(x) = x sin x satisfies the following equation: P"(x) + (x) + t cosx = of t is

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

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Q: Find a particular solution y, of the following equation using the Method of Undetermined…

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Q: 7 Solve the differential equal (c) f"(t)-f(t) = u(t) sin 3t-(t-4) sin 3(t - 4) where f'(0) = f(0) =…

A: Some of the properties of Laplace transformation .…

Q: If cos-x y, then sin(2y) Is equal to 2r O 2/1- x2 2r VI - x? 2r1 - x? O dt atr = 0 has a The…

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Q: 3 f(x) = x° – cos(x) Solve this question by the Newton-Raphson method on the topic of solution of…

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Q: 1 Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

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Q: 10) Find the linear approximation to g(y) = Cos(y+1) at y = 0. Use the linear approximation to…

A: Here, the given function is: g(y)=cos(y+1) To find the linear approximation of g(y) at y=y0=0 using…

Q: 11. z= e* cos y 12. h(x, 1) = e sin(x + 51)

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Q: 4.2 Given g(x) = ) = cos z + sin for 0 <<, find the value of f(x + 1)dg(x). END

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Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: 12 1 3. Find the exact value of the definite integral | dx (x+6) Vx- 3

A: The given definite integral can be evaluated using the method of substitution by making the…

Q: 1 y = 5 sin x + 3 cos x at the point (0, 1/3). The equation of this tangent line can be written in…

A: Here a function is given and we have to find the equation of the tangent line in the form y=mx+b at…

Q: 1+2 e-kt cos kx = k=1 sinh t - cosht cos x

A: To prove / disprove: 1+2∑k=1∞e-ktcoskx=sinhtcosht-cosx

Q: (1) f(x, y) = e-(r²t;2 ) (2) f(x) = (x – sin(x))2

A: Note: "Since you have posted multiple question. As per our guidelines we are supposed to solve only…

Q: f (x) = xe-* – sin?x Newton Raphson (1st Method) @ x1 = 0.5 Newton Raphson (2nd Method)@ x1 = 0.5…

A: Newton Raphson Method:- Hence by Newton Raphson Method Root of the equation is 0.61447 (correct…

Q: 4. Solve for ſ e* sin x dx in the equation S e* sin x dx = e* sin x + e* cos x - Se* sin x dx + c.

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If an answer does not…

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Q: i) Given that f(x)=3cos5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a <90°.…

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Q: Find a particular solution y, of the following equation using the Method of Undetermined…

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Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: We have to find Perticular Solution for given differential equation by method of undetermined…

Q: Using the method of undetermined coefficients, find particular solution for y"''+y"+y'+y=e* +sin x…

A: Given y'''+y''+y'+y=e-x+sinx-x+1. Let us compute the complementary function first,…

Q: 1. L 16x dx 2. o &. + 2 +1 3. (sec x- tan x dx dx 4. cos x tan x 1/4

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Q: 2. Solve for y in the equation y = e* sin x + e* cos x – y +c 3. Solve for f e* sin x dx in the…

A: Given, (2) y = exsinx +excosx -y +c  We have to solve for y (3) ∫ex sinx dx = ex sinx + ex cosx -…

Q: Q/ solve the differentil-equation ty-f'sinx-x)+(3xy+2y.cosx)

A: We will solve the problem.

Q: 7. Determine the lowest positive root of f(x) = 7 sin(x) e-* - 1: a. Using Secant Method with…

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Q: Find F

A: Given:

Q: 2. (a) Show that V3 cos x-sin x COS where 0<x<2r . 2 (b) Using the result in (a), solve the equation…

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Q: .1 Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

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Q: Find values for the constants a, b, and c that will make ƒ(x) = cos x and g(x) = a + bx + cx2…

A: Consider the following functions: fx=cosxgx=a+bx+cx2 f0=g0cos0=a+b×0+c×021=a+0+0a=1 Hence, the value…

Q: 1 1. The function Y = sin(t² )+ 4 is graphed below. Define F(x) = [, sin(1²) + - 1 dt 4

A: Given: F(x)=∫0xsint2+14dtThus, Fx represents the area under the curve y=sint2+14(a) First of all we…

Q: 3. A 2 cm long metal wire with thermal diffusivity ² = 4cm² s¹ is used to conduct heat in a machine…

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Q: f(x) X-Cos(X) ✓ Tol = 0.0005 ||X₁ = 1 1 + x 2 By using newton rafson find the solve...

A: We have f(x)=x-cos(x)1+x2,  x0=1 f'(x)=(1+sinx1+x2)-(x(x-cosx)(1+x2)32)  (using product rule of…

Q: 1. True or False a. The output of the cotangent function is always a number between-1 and 1. b.…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: 9x²– e2x 2 Given by a function of x is equal to v1 – cos²x + where f(x) 3x+ e* = 0. find the roots…

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Q: 4. The given equation sinh(xyz) = x + y + 3z implicitly defines a differen- az tiable z as a…

A: Differentiate with respect to x keeping y as a constant.

Q: f(x) X- COS(X) 1 + x 2 By using newton rafson find the solve.de ToL = 0.0005 1 X₂=1

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: Find C co that the line y = 4x + 3 is tangent to the curve y = x2 + C.

A: We can solve it using differential equation as below.

Q: Given the differential equation (2r cosx – 1)r'=r?sin x, obtain the value of U = M dx A U=-r-sin x…

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Q: e) f(x)=tan(cos¹.x) () COS X [+sil x h) y = 2

A: Given

Q: Which of the following methods can be applied to find a particular solution yp of y"+y=cos(e-x)? A)…

A: Solution :-

Q: 2 S tan x sec x dx e-0.3x =27 Q5) (A) Evaluate (B) Solve for x: |3D

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Q: y' cos x + y sin x = 2cos x sin x- 1 What is the particular solution when y(Tt/4)=3v2

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Q: Q1: Find an expression of for the function y dt 2t %3D + 3x*. 3x Q2: Find an expression of for the…

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Q: 7. A particle travels on the x-axis so its velocity at time t is given by v(t) = ÷- sin t, for 0 <t…

A: In the question it is asked to calculate value of time t for which the particle moves to the right.

Q: (c) 1. f(t) dt = In(x) cos(x)+ sin(3) L e-" f(t) dt, find f(x). You may find FTC 1 useful. sin(3)…

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Q: 10. Give the differential of f(x) =x² - 3x at x = 1 with respect to the increment 1/10. 11. Use…

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Q: به)ک ن ان -)f Ssin*(x)cos°(x)dx du )کی + 207 - )J No appropriate Match au)قی - 207 - ه-)J du )کی +…

A: Find the integral match of the integral sin5xcos5x.

Q: 2. By using Simpson's rule with N = 4,8, and 16 Integrate the following functions SOLVE PART B eX…

A: We need to use Simpson's rule to evaluate the integral. So, we need to find ∫0π4Tan X dX If we need…