Solve the given initi al value problem using the method of Laplace trans form ylo) =0, y'lo) = | 10. "+ q y = glt), where glt) = 0stくa 18 if a st

Q: What is the unit tangent vector to the curve r(r)=sint i+2cost j when t=π/4

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Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: 20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so…

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Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: Find Laplace 2 2 [sin(34) + 65inh czt) ]

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Q: Given f(x,y)=ln(x^2+y^2) a) determine Dv f(2,3) with v = b) what is the angle, in radians, between…

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Q: 2 : Let a(t) be a unit speed curve and define B(s) =| Ba(t)dt, where Ba is the binormal of the curve…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: aくtく2 -6(ft) whee f(t)=$°. e" 25t * X(ult-aJca(t-z)

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: 1. Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), -5 ≤ t ≤ 5 b) r(t) = √ēti +…

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Q: Một chuyển động có phương trình: R(t) = (cos(4t))i + (sin(4t))j + 4tk. Tìm vector tiếp tuyến đơn vị…

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Q: 2 write Dirac Delta beinction and it's laplace trans forms.

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Q: Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental…

A: 1 Consider the paraboloid parameterized by σu,v=u,v,u2+v2. We have to find the second fundamental…

Q: et u = e Sin P= sin sc Lind su using chain Rule

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Q: Laplace £& cos'at} Cos al t 81

A: The Laplace transform of the function f(t) is represented as F(s), it is defined as ∫0∞e-stf(t)dt.…

Q: Find the laplace Sf fhe fanction: ft)esint u lt-) )= where ult- T) is aunit | tunction fur

A: We have to first use property of Laplace transform.

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: 7) Find the unit tangent vector for the parameterized curve: r(t) = cos ti+ sin tj+ sin tk, 0≤t< 2π

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Q: What was the 1-hour growth factor for the bacteria's mass?

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: The curvature of r = 1+ cos 0, 0: 2 2/2 5 2/2 3/3 2 3/3 3.

A: Given: r=1+cosθ,θ=π2 κθ=2f'θ2+fθ2-fθf"θf'θ2+fθ232   r=f(θ)r=1+cosθ f'θ=-sinθf"θ=-cosθ

Q: 4. Find the unit tangent vector T(t) at the point with the given value of the parameter t: a) r(t) =…

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Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: Solve the problem by using Laplace Trons form +y= Sin 2€ %3D yo) = 0

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Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: Consider the function f( + ty)- 3z²y+i ain z nw that thin funeticon does not satisfy the…

A: a) The given function is: fx+iy=3x2y+isin x Cauchy Riemann equation:  Let fz=u+iv be a complex…

Q: Detemine the lineality over a full langth in the a-direston of he wave Sine Curve y- Asina

A: We know that the wave length of y=A sin x is 2π.  Note: The linearity over a full wave length of the…

Q: Show that u is s is mmomphie to F' Lt T:VaV (V is as abore let Tuct) zt u'Le) 2 the derivative im…

A: Let F=ℝ and V=a+bx2+cx4 :a,b,c∈ℝ . Show that V is isomorphic to F 3. Let T: V→V defined as follows,…

Q: tind Yaduis ot curuature of the Curue O r= 2t i t (1+); - 2t k at (2,1,-2) 13 Brofi+tietk at the…

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Q: What is the Laplace tranform of (e4t - e13t)/(6t)

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Q: b) Find the laplace trausform of the Runction fCE)= sint.ult - Tt) where u(t-. is a unit function.

A: Here we have use property of Laplace transform when multiplied by shifted unit function.

Q: 3 s? + 4) s\s

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Q: Find the Laplace flt)= 3t. - 5°cos 3t

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Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: 10. 11. Find a unit normal to the vector d = [3, −4] a) ₁ = [₁] b)= [₁] ©^=[²] • ñ = [§ › }] /] c) â…

A: 10) Given that  .We  have  to  find the unit  normal  vector  to  the vector  Note that Then, So,…

Q: 53-S²+S-1

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Q: SUPpose that xay Casy x3 =9 ) FInd the derivative of eaichterm with respect to X b) far dy lax Use…

A: Given x2y + cosy + x3= 9

Q: 5. Find the total length, curvature and torsion of a curve: [cos² t,sin² t, 0] 0≤t≤n?

A: We find total length, curvature and torsion