af and If f(s, t) = t sin st, find - as at

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: Compute r"(t) and r(t) for the following function. r(t) = (cos 2t, sin 3t, cos 6t)

A:

Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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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: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

A:

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: If r (t) = (sin(t), cos(t), 2), then ſr (t) dt = 0.

A: The vector function is given by rt = sin(t),cos(t),2 To evaluate : ∫0πrtdt

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 z = 2 cos t + 26 and y = 5 sin? t dz dy dy dz

A: Derivative of function in parametric form

Q: Let r(t) = (et, t2 + 1, h(t)). If |r' (0)| = √2, which of the following is a possible h(t)? O sin(t)…

A:

Q: dw when r= 3 and s = - ar 3 if w = (x+ y + z)“, x=r-s, y= cos (r + s), z= sin (r + s). Find

A:

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

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Q: 2. Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a.…

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Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –…

A:

Q: Find r(t) and v(t) if a(t) = 8 cos(t)k, v(0) = 4i + 6j, and r(0) = 7i. v(t) r(t) %3D

A: We have given: at=8cost kv0=4i+6jr0=7i We know that at=dvtdt So, we can write this as: dvt=at…

Q: If f(x) = 2 sin z +9 cos z, then f'(z) = f'(4) =

A:

Q: Evaluate [P r(t) = (t, sin(t), cos(t)), 0 ≤ t ≤ F. dr where F = (4z, - 3y, 2x), and C is given by

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Q: Compute r"(t) and r""(t) for the following function. r(t) = (cos 4t, sin 2t, cos s 6t)

A:

Q: if z sin とこ3r'+25 , Y=4イ-ス3 Z = 2r-35* W= Z Sin %3D * find aw,w ar me' me as

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Q: et sin t? blas Y - et cos t? lio -n/2 <t < 0

A:

Q: c) If f(x, y)= e" cos 2x, then show that = 0.

A:

Q: d(x,y) x(u, v) = sin(u) + cos(v) and if a(u, v) y(u, v) = – cos(u) + sin(v). 1.

A: Given xu,v=sinu+cosv and yu,v=−cosu+sinv We have to find the Jacobian ∂x,y∂u,v. The Jacobian…

Q: 2. Given that z and w are independent variable and dependent variable dz respectively, obtain dw a.…

A:

Q: If r (t) = (cos(t), sin(t), 2) r(t) = (cos(t), sin(t), 2) , %3D T then fr (t) dt =

A: It is integration using limit problem.

Q: Evaluate [P F = (4%, F(t)= (t, sin(t), cos(t)), 0≤ t ≤ T F. dr where 3y, 2x), and C is given by

A:

Q: If r (t) = (cos(t), sin(t), 2) , then fr (t) dt %3D

A:

Q: Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a)…

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Q: Solve the following equation: 4 - Urz = 0,0 < x < T,0 <t < ∞ u(0, t) = u(T, t) = 0 %3D | %3D %3D…

A:

Q: . Solve the following problems: (a) Utt = 0, 0 0, u (x, 0) = x + sin x, Ut (x, 0) = 0, 0 0.

A: Solution

Q: Let P = {x € R | sin(x) = 0} and Q = {na | n E Z}. What is the relationship between P and Q?

A: Let P = {x ∈ R | sin(x)=0}, and Q = {nπ | n ∈ Z}. What is the relationship between P and Q​

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: Given z = 2 cos t + 23 and y = 5 sin?t dr (i) dt (ii) dt dy (iii) da

A: Explanation of the answer is as follows

Q: If r (t) = (cos(t), sin(t), 2) , then ſr (t) dt =

A: r(t)=&lt; cos(t), sin(t) ,2&gt;

Q: If Y(t) = X(t + a) – X(t – a), prove that R, R. (T- 2a). Hence prove that Sy„(@) = 4 sin“ ao S„(@) =…

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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: Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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Q: F k d

A: Use conic section we can prove it.

Q: Find the function r that satisfies the given condition r'(1) = (e!,c . r(0) = (5,5,5) Cos t, sec…

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Q: S™ sin dt Sa" 2 1 b. 2 С. 3 d. None of the above a.

A: Given that, I=∫02πsint2dt we have to find the value of given integration.

Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

A:

Q: If sin ) is an antiderivative for f(x), then s? f(x)d(x) =

A: We have sin1x2+1 is an anti-derivative for f(x)

Q: z{cos (: -)u(: - )} = a) 3 3

A: We find the given Laplace transform. Formula:  L{cos(at)}=s/(s2+a2)......(1)…

Q: If r (t) = (sin(t), cos(t), 2). then ſr (t) dt =

A: we have to find the following

Q: Given w= (x+ y+z) , x=r-s, y=cos(r +s) , and z = sin(r +s) , %3|

A: Given  w=x+y+z2x=r−sy=cos(r+s)z=sin(r+s)

Q: Compute r" (t) and r"(t) for the following function. r(t) = (cos 3t, sin 6t, cos 2t)

A:

Q: dz az If z = xyeX/Y, x = r cos(0), and y = r sin(0), find and ar when r = 2 and 0 = %3D az ar (r, 0)…

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Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

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Q: If sin t 2 and t is in the 3rd quadrant, - then cos t = Vī6 V34 5 Vī6 3 Vī6 | Vī6 3

A: Given Sin t=-(3/5) t =is in the 3rd quadrant Find out  cos t=?

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 r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

A: