4 Given F(r, s,t) = r (7sª + 7t°), compute: Frst

Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

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

A:

Q: Consider I = f(x)dx. The approximation of I using composite trapezoidal rule with 3 subintervals is…

A: The trapezoidal rule is given by  I=∫abf(x)dx=h2y0+2y1+y2+...+yn-1+yn   where h=b-an given that…

Q: Scalar line integrals Evaluate the following line integral along the curve C.

A: Given integral is Parametric equation of semicircle is

Q: Given y = s, s = 20 – v? and v = -2t, dy determine at t = 1 dt A V3 в 2 с 1 D-1

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Q: stw j X = Sin (stw,y< %3D z= Stttw, find f

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing the same.…

Q: The linear approximation at r 0 to sin(2r) is A+ Br where A is: and where B is:

A:

Q: Given that F(x, y, z)=sin xi+ cos yj + xzk. Evaluate ſ. F.dr where C is given by r(t)=( r', –f,t) ;…

A: Given that

Q: Integrate counterclockwise dz by Cauchy's formula z2 – 16 counterclockwise around the circle C : |z…

A:

Q: dw Q/Answer the following - ar ,w = (x + 3y + z)², x = r3 – s², y = tan(r + s) ,Fsin(r+s) at the…

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Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: The linear approximation for f(x,y)=Vy+cos?(x) at (0,63) is O L(x.y)=(65+y) 16 L(x,V)=(65-y)

A:

Q: 3) Evaluate, to the nearest hundredth, 11. (V x F) dS where F = and S = {(x, y, z)| 2² − 1 = 3x² +…

A: Here we will use Stokes theorem  According to stokes theorem  ∫∫S∇×F.dS=∫CF.dr C is the  boundary…

Q: Find r(t) that satisfies the initial condition(s).…

A: Given: r(0)=2i

Q: Given that f"(x) = cos(x), f'(T/2) = 8 and f(T/2) = 7, find: %3D f'(z) =O %3D f(2) =U

A:

Q: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

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Q: 4. Evaluate S. (z – 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: Contour integrals or line integrals along a path C   can be written as ∫Cf(z) dz=∫abf(z(t) z'(t) dt…

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: "III. Vf dr = , where f = xy²z and Cis given by r (t) = (t +1, t², t³),0<t<2

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Q: Q.4 (a) Use the formula S.{f"(z)} = af(0) – a*S.{f(x}} to find Sa{cosh(2r)}. (b) Classify the…

A: Given In part4a:Sαf''x=αf0-α2SαfxIn part4b: yuyy-xuyz+uy=0

Q: Q3: Given T(u) = sin (u), where u = /x2 + y2, find T- Ty. %3D

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Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: Q3 Given that w = x + 2y + z²,x = = ,y = r2 + In s, z = 2r X%3D %3D aw aw and ar Find as

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Q: Q2 Given z = xw? + cos y + wx , w= t , x = 2t2 , and y = 3t, find dt

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Q: Let f(r, y, 2) = 2ry + 2. Evaluate f(1, y, 2) dz where C is the portion of the helix r(t) = cos ti+…

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Q: 41. In each part, confirm that the stated formula is the local linear approximation at (0, 0). 2x +…

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Q: ∫C  ez / (z - πi) dz where C is defined as z(t) = 2eit and 0 ≤ t ≤ 2π

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Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

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

Q: Given f(x, y, z) = V 42? + 6y² + 3z², find fz(x, y, z) = fy(z, y, z) = %D f:(x, y, z) =

A: we need to find out partial derivative of first order

Q: Given that f'(t) = 2sint + sec?t ,– t and f(0) = 4, find f(t) ドIN V V ドIN

A: Given, f'(t) = 2sint+sec2t  f(0) = 4 Formula used: Integral of sint = - cost Integral of sec2t =…

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: K is between J and L, KJ= 46, and KL = 47. Find JL. Y f(X) Vx X,

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Q: Prove that r(v) : dx, v> 0.

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Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

A:

Q: Find fr(r, y) and fy(x, y) given f(r, y) = tan r - cos(r² – y²).

A:

Q: Write proofs in two-column form.

A:

Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

A:

Q: What is v(t,) at t, in the given equation of s below? Also, what is v(t,) if t = 3? s = vt +1 1 1 ;…

A: Given s=t+1

Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?

A: Given that: x=15ln ty=225 t2

Q: What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

A: The particle is following the trajectory (x(t), y(t)). Velocity across x axis = Vx = Rate of change…

Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

A:

Q: Use the Chain Rule to find dz/as and əz/dt. e cos(0), r = st, 0 = V 56 + t6 || dz as az

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Q: dv E={my,)|→<y<4Y<そく4, Osns? そ

A: Given that  Triple integral of z/(x^2+z^2) To evaluate the integral

Q: f(z, y) – zsiny +e, then Vf(r, y) (0, e").

A:

Q: Q2 Given z = xw? + cos y + wx , w =t, x = 2t? , and y = 3t, find dt

A: Let's find.

Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

A:

Q: P to the line L is equal P that is orthogonal to t

A: Given as, The distance is given as, d=AP→sinθ