(a) Find the Laplace Trans form of f (t) = 2u(t+1)cos² i+e"8(t-2)

Q: Find the laplace of  f(t) = cos(root2)t + sin (3t)

A:

Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

A:

Q: Find T, N and B for the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) at the point t = 0 Give your…

A: Given that, r→t=4 cos 5t,  4 sin5t,  5t  at the point   t=0

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

A:

Q: Find T, N and B for the curve 7(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 %3D Give your…

A: given that                                          r→(t)=4cos(2t), 4sin(2t), 2t at t=0…

Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

A:

Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

A:

Q: + dy-39 sin ax y co) y'o) =12

A: Laplace transferom for the differential equation

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: Xexs is The Laplace inverse of s2+4x? O a. sin(2x(t-1)) 5(r-x)dr 0.

A: Let f(t)=L-1xs2+(2x)2           =x L-11s2+(2x)2          =x.12 sin(2xt) ∵L-11s2+a2=1asin(at)…

Q: which one of the pairs are linearly dependent? a) O f(x)=e*, g(x)3xe b) f(t) =t and g(t) =t² c) f(t)…

A: Two functions f(x) and g(x) are linearly dependent if there exists a , b , both not equal to 0 and…

Q: Find 7, Ñ and B for the curve (t) = (4 cos(3t), 4 sin(3t), 2t) at the point t = 0 Give your answers…

A: We have to find the  for the given curve.

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: How do I solve the laplace(u(t-2)cos(t-2))

A: The Laplace transform formula for translation on the t-axis is given by ℒ{u(t-a) f(t-a)} = e-asF(s),…

Q: Find pairs of solutions of Laplace's equation, =0, based on these complex functions (a) ze2, (b) z*:…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3 Substitute Z=x+iy in Ze2z…

Q: Find the domain of the vector function 7(t) = Domain: {t| <t< }

A:

Q: 1. Use formulas (2)-(5) to find the Laplace image of the given function (a) 2e-3t (d) 7sin4t - 1 (g)…

A:

Q: 1. Use formulas (2)–(5) to find the Laplace image of the given function (c) 5e²t - 2t3 (f) 1+ sin…

A: Laplace transformation of the functions

Q: Compute the derivatives of the given functions. d. a) dt d [5 sin ¹5t = FI

A: As per the Bartleby guidelines, answering only first question as the other questions are not the sub…

Q: Find (cost using Laplace find [[ sint] using Laplace

A: Here we can use following formula of Laplace transform 1. Lcosat=ss2+a22. Lsinat=as2+a23. Lftt=∫s∞Fs…

Q: Consider the curve defined by r(t) = (cos(t) + t sin(t))+ (sin(t)- t cos(t))] for t > 0. (a) Compute…

A:

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…

A:

Q: laplace(u(t-2)sin(t-2) )

A: laplace(u(t-2)sin(t-2) ) = e-2ss2+1

Q: Find T, N and B for the curve r(t) = (4 cos(3t), 4 sin(3t), 4t) at the point t = 0 Give your answers…

A:

Q: '(t) = ( T(t) = ( r(t) = (4 + 31, 2 - 21,9 + 6t). ). ).

A: Given: To Find: To determine .

Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

A: