has at least one solu Prove that the equation r+ sin(x) = VI +3 %3D (0, т).

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

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Q: FIND THE GIVEN DIFFERENTI Homogeneous Eguation ( 3x + 4y) dx - dy -0

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Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: 8. If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dtat t = 0?

A: Chain Rule d(f(g(x))dx   =   f'(g(x)) . g'(x) We have given r = sin(f(t))        f(0) =  π3  ,…

Q: To compute sin (3t) cos" (3t) dt, first you need to I Select) * then subsitute u = [ Select ) * and…

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: I need help to find particula solution using undetermined coefficients: y''+4y = sin(t) + t2 + et

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Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

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Q: make the given substitutions to evaluate the indefiniteintegrals. ∫sec 2t tan 2t dt, u = 2t

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Q: S cos“C)dy

A: NOTE: Refresh your page if you can't see any equations. . take

Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: (t – sin t)v1 – cos t dt

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Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: Sect sec't dt Tari'la)

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Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x – 4 sin°x .…

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Q: 1. ò F 2 dt dt Ve' + 9

A: The integral function are 1. ∫etet+9dt   2.∫2t+4ttdt

Q: If f cos xdx = A + B sin x + Csin²x+ Dsin³x+ E sin*x+ Fsin5x, what is the value of A + B + CD + E +…

A: Consider ∫cos5x dx =∫cos4x cos x dx =∫(cos2x)2 cos x dx=∫(1-sin2x)2cos x dx…

Q: (1 + cos 7t) 2 sin 7t dt

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Q: On what interval is the solution of the IVP cos e (1+ sin 0) y (0) = 2 - 47 valid?

A: Given IVP is dydθ=1cosθ1+sinθ y0=-12 Now,  dydθ=1cosθ1+sinθ dy=1cosθ1+sinθdθ∫dy=∫1cosθ1+sinθdθ

Q: 3. If v = sin- (4) + tan-' (±), find the value of r + y. 4. If z= ear+by. f(ax – by), prove that b…

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Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

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Q: In the equation where y" + 4y = 0, A. Show a solution for all the values of the arbitrary constants…

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Q: Use Part 1 of the Fundamental Theorem to simplify the following expressions.

A: According to fundamental theorem, to find the derivative of the integral, one need to plug the upper…

Q: Solve for the General Solution ds 5s = dt te 5t sin t %3D

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Q: ds 1 s tan =cSC dt 2 2 2

A: We will find out the required general solution.

Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

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Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: 5. J sin42x cos22x dx.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: (b) Calculate e cos(Tx) dx using integration by parts as many times as necessary.

A: Given: ∫excos(πx) dx The formula for integration by parts is given as…

Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: The linear approximation at x = 0 to sin (7x) is A + Bx where A is: and where B is:

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Q: The linear approximation at x = 0 to sin(4x) is A + Bx where A is: and where B is:

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Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: Use the method of characteristics to solve the first order equation Ug – 2uy = 3 with u(x, x) =…

A: Method of Characteristics and General Solutions: The general solution of the quasi-linear equation…

Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x- 4 sin'x.…

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Q: Using a similar method to above, that is, integrating by parts twice, the following result may be…

A: In this question we have to prove Integration by using Integration by parts.

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

A: