If lF· dĩ = L, where C : x = 2 cos t, y = 3 sin t, t E [0, 7], type in the value of fe F · dī where C : x = (2 – 4 cos? t), y = 6 sint cos t, t e [0, 5] in terms of L and motivate briefly in words. If it is not possible to determine, give a brief reason.

Q: Let y(x) be the solution for the DE. y+y tan(x) + sin(x) =0 If y(0) = In 2, then at x = the value of…

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Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

Q: | sin ædx =? cos z +c O A. – cos x + 2 cosz - 2 4 O B.-z+2를-를 +c В. O C. cos ¤ – 2 cos" z + cosº z…

A: Consider the given integral. ∫sin5x dx Rewrite the integral. ∫sin5x dx=∫sin4x·sinx dx…

Q: (c) x(t) = eat cos s wtu(t), a > 0 (d) x(t) = e-af sin w,tu(t), a > 0 %3D

A: Let xt is a function. The Fourier transform of the function xt is denoted by Xiwor Xf and defined by…

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0)

A: We can find the answer as below.

Q: (23) If f(x) = sin zx, find the value of fe (x). 23 sinx %3D 23 e. sin x a. 23 b. cosx . 1 cos TEX…

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Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0). Leave your answer correct to two decimal…

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Q: (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh a sin y. (e) | sin z|? = sin² x + sinh? y, (f) |…

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Q: If f(z, y, z) = sin(z) +ay2-23 then the value of a that makes div(Vf) = -sin(z) - 6z is Answer

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Q: won of cos 0) dr + r (sin 6 + cos 0) rsine rcose = C O r + rsine rcose = C 5 + rsine rcose = C r2 +…

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Q: 52. If z = f (x, y), where x = r cos 0 and y = r sin 0, find a. Əz/Ər, b. дz/80, and c. d z/Ər d0.

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (b) z = x2 + 3xy + y2 ; x = sin s + cos t, y = sin s - cos t

A: Consider z=fx,y & x=fs,t, y=fs,t Then, the derivative of z with respect to s is given by:…

Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find f,(1,2,0). Leave your answer correct to two decimal…

A: We can find the answer as below.

Q: The general solution of + ytan x = sec x is dx A y = sec x + C sin x В у (sin x - 1) %3D С y= sin x…

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Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f;(5,5,0).

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Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f,(8,2,0). Leave your answer correct to two decimal…

A: Partial differentiation of f(x,y,z) with respect to x is calculated by treating y and z as…

Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

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Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

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Q: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

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Q: If r(x) = -cos (x + 9) +7, determine the antiderivative of r(x). (Do not include the constant C'in…

A: In this question, we want to find the antiderivative of the given function r(x).

Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: -cos x + sin x in the form r sin (x + a), where r> 0, is: e A. 2 sin x+ -sin |x+ 4 B 57 2 sin x+ 4 2…

A: We will find out the required expression.

Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: What is the general solution of sin z sin ydr + cos zcosydy =0 tan z = C sin y + cos r + C sin z = C…

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Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find f:(5,5,0).

A: This question is based on Partial derivatives.

Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: 23. sin r cos? "x dr ².

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Q: Simplify your expressions for xM(t) = 0.5 cos + 9cos ( & ym(t) = 0.5 sin + 9sin xM(t) = B cos(kt +…

A: xM(t) = 0.5 cosπt3 +9cos πt6yM(t) = 0.5 sin πt3 + 9 sin πt6 XM(t) = B cos(kt + β)YM(t) = C sin(kt +…

Q: 1) Given x = Vu2 + E2 sin 0 cos 2 y = yu? + E² sin 0 sin 1 z = u cos 0 ds? = dx2 + dy2 + dz2 %3D…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to others then…

Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: Find a particular solution yp(x) to the equation y′′ + y′ − 2y = 5 sin x in the form yp(x) = c1…

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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: Which is equivalent to ſ sin y cos(/2) dy? C/2) dy? a.) S [sin("/2) – sin ("/2)] • dy b.) S sin("/2)…

A: The given integral is: I=∫sinycosy2dy As according to trigonometric formula:…

Q: Given: f(x, y, z) = e¯ª sin(yz) Find: ² f(x, y, z) əyəx O z cos(yz) et O cos(yz) e O-ze-* cos(yz) O…

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Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: 8. (e' + 2) sin x dx – e' cOs x dy = 0 Ans. (e' + 2) cos x = C dy et-y +x?e¯y Ans, e = e* +: +C 3 9.…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: For how many a E (0, 1) will sin(x) + a sec(x) = cos(x) + a csc(x) have at least two distinct…

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Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

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Q: What is the general solution of (r + sin 0 cos 8) dr + r (sin 0 + cos 0) d0 = 0 ? %3D rsind rcose =…

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Q: 7. Determine the following general antiderivatives. | cos*(x) b. sin(x) xp- 10 10 | sin(x)cos(x)] d.…

A: Please see the below picture for detailed solution.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.