x = Cịcos (At) + C2 sin (At)

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

Q: 3. Obtain in two ways the general solution of (r + sine - cose ) dr + r (sine + cose ) de = 0

A: Use substitution method

Q: Suppose that 1 a + sin x ) dx = 15x 1 + x2 -1 What is the value of a Your answer should be an…

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Q: nd all values of x in the interval [0, 2x] that satisfy the equation. (Enter your an 9 sin(2x) = 9…

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Q: 2 y = A cos 4x + B sin 4x +sin 3x b) 7

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Q: Find all values of x in the interval [0, 2π] that satisfy (cos x)2 − 3 sin x − 3 = 0

A: x=3π2 is the only values that satisfy the given condition see the calculation below

Q: Find the iterative scheme for the root of equation cos x- 3x+1=0 by Newton-Raphson method. O a. None…

A: Newton rephson method problem....

Q: Determine the exact x– value(s) of the intersection points of the functions f (x) = 4 sin² +7 sin 4…

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Q: 5. Use Newton-Raphson method to find solutions accurate to within 10-2 for x - cos x = 0 on [0,…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

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Q: 10. Suggest ways to avoid loss of significance in these calculations. (1) Vx² +1-x; (3) sin x- tan…

A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: If k 0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to ¹(3 cos(kr) cos³ (kr)] + C

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Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

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Q: ¥2/3 6. cos'x sin x dx 5.

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: Evaluate the given function tan²ydy = sin3 xdx is equal to.. 3(tany – y) 30 + cosx А. Зх - cos³x…

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Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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

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Q: 22. y' = 1 + 3y tan x. ANS. 3y cos³ x = c + 3 sin x – sin³ 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: 5. The function f(0) = (sin O+cos 0) + (sin 0– cos 0) may be written as

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: Show that where n is a positive integer.

A: To show

Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: _5. In the equation y = sin-1 x, if = , then y= TC %3D %3D %3D

A: 5. In the equation y=sin-1x , if x=12 , then y=π6. The given statement is True, The reason regarding…

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

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Q: Show that y = sin x, y = cos x, and y = a cos x + b sin x (aand b constants) all satisfy the…

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Q: (5) Find the local extreme values of the function h(x) = sin?x – V2 . sinx + 2/2 on the interval (0,…

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Q: Activity 2 Differentiate the following. 1. y = sin(6x) 2. y = sin (5x – 2) 3. y = tan (2x³ + 5) 4. y…

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Q: 3) If y = sin(2n), and x = cos(2n)

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

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Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: The result of solving the integral x' tan(x²) dx is: A) Inlcos(x) +c B) tan(x)-+ In/cos(x²)|+c D) +1

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Q: Where does the periodic function f(x) = 2ešin (x/2) take on its ex- treme values and what are these…

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Q: 1) fcoe cos x sin rdr

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Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

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Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below

Q: 2. Is it possible to write sin (37x) as a linear combination of sin(2rx) and sin(Tx) for all values…

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