Show that cos(wt – B), cos wt , sin wt are linearly dependent functions of t.

Q: Find the differential of each fuction. a) %3D dy= ? b) U COS U dy= ?

A: Given,  (a) y = s7+8s  (b) y = u cosu  We have to find the differential of each function.

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: (c(2z+y), %3D ue of c in the joi F of W.

A:

Q: Show that z=tan-1(2xy/x^2-y^2) satisfies the Laplace equation

A: The given equation is, z=tan-1(2xyx2-y2). Obtain the partial derivative of z with respect to x as…

Q: þ/ Show that the function satisfy Laplace equation f(x,y) = In /9xy+3y²

A:

Q: Find the linearizations of the functionsat the given points. ƒ(x, y, z) = √2 cos x sin ( y + z) at…

A:

Q: (a) Find the gradient and Laplacian of the scalar function T(r,0,¢) =r(cos0+sin0cosø)

A: As two questions are given I will solve only the first: We are given: T(r,θ,ϕ)=r(cosθ +sinθcosϕ)…

Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

A:

Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

A:

Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: find the decomposition of a(t) into tangential and normal components at the point indicated r(t) =…

A: The given vector  rt=t,cost,sint ,      t=π2 To finding the components of acceleration take the…

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: Sketch the direction field of the D.E. y = y - t and the solution curves corresponding to y(0) =-1,…

A: Solution of question is written in below steps.

Q: Find the linearization L(x,y) of the function f(x,y) = e (X cos (5y) at the points (0,0) and 0,- 2

A:

Q: find the decomposition of a(t) into tangential and normal components at the point indicated, as in…

A: Given: r(t)=(t,cost,sint)t=π2

Q: 2. Let F(t) = (e' cos t) î+ (e' sin t)j+ek. a. Find symmetric equations of the line tangent to the…

A: Given:  F→t = et costi^ +et sint j^ +et k^  To Find:  Symmetric equations of the line tangent to the…

Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

A:

Q: Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y =sint cos…

A:

Q: Determine whether the functions y, and y, are linearly dependent on the interval (0,1) y =1-2 sint,…

A:

Q: Let f(x, y) = 8x + 2y2, r(t) = (cos(t), sin(t)). Use the Chain Rule to calculate f(r(t)). !! dt…

A:

Q: Show that the function f(x, y) = e-2y cos 2.r satisfies the Laplace equation.

A: use partial derivative to check whether it  satisfy the equation or not

Q: Show that the function f(x, y, z) = x² + y? – 2z² satisfies the Laplace equation.

A:

Q: Verify by differentiation that a) / t dt : V1+t2 /1+t² + C; _ b) tan(x)dr = – In(cos(x)) +C, –1/2 <…

A: Given to find ∫t1+t2dtPut 1+t2=udifferentiate 2tdt=dutdt=du2therefore…

Q: apply linearity property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: f(t)=t cos 2tf(t)=t2 e-3t

Q: Show that the function f(x; y; z) = 2z3- 3(x2+y2)z  satisfies the Laplace equation.

A:

Q: If g(x) = | cos' t dt , then determine g'(x). %3D

A:

Q: 1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

A:

Q: 9. Demonstrate that the functions Y1 = x2, y2 = sin(x), y3 = xe are linearly independent on R.

A: Recall: If y1,y2 and y3 are the given function and         Wy1,y2,y3x = y1y2y3y1'y2'y3'y1''y2''y3''…

Q: Show that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.

A:

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: Find the linearization L(x,y) of the function f(x,y) = e* cos (9y) at the points (0,0) and ...

A:

Q: Show that if the function f(x, y) = ecos-e-cosx, satisfies Laplace Equation.

A:

Q: The functions cos r and cos- are linearly dependent (0, ) on

A: evident from the two curves that after zero in a positive direction the two graphs coincide with…

Q: Let T = x²y - xys + 6x, where x = r cos 0 and y = r sin 6. Use the chain rule to find dT/00.

A:

Q: Show that U(x, y) = e"cos v,V(x, y) = e"sin harmonic of each other if f = u + iv is analytic. v are…

A: Given: The function f=u+iv is analytic.   To show: Ux,y=eucosv and Vx,y=eusinv are conjugate…

Q: Show that the function f(x, y) = In /x² + y² satisfies the Laplace equation. %3D

A:

Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: Find F(s). F(s) L{cos(6t) U(t - π)}

A:

Q: If g is the vector-valued function defined by g (t) = (sin(2t), cos(3t)), then g' (t) = %3D

A: Given : gt = sin2t, cos3t

Q: Let F(t) = (e' cos t) î+ (e' sin t) ĵ + e' k. %3| (a) Find symmetric equations of the line tangent…

A:

Q: Show that the function satisfy Laplace equation f(x,y) = In /9xy+3y² %3D

A: We need to show that the function f(x, y)=ln9xy+3y2 satisfies the Laplace equation. Now,…

Q: Show that cos(cot – B), coscot, sincot are linearly dependent functions of t.

A: We have to check

Q: The two functions y1(t) = sint cos t and y2 (t) = sin 2t are linearly Independent. True False

A: →Two functions y1 and y2 are said to be linearly independent,                 if, y1 ≠k y2 , where…

Q: how that the function satisfy Laplace equation f(x,y) = In /9xy+3y²

A:

Q: se Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit…

A:

Q: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…

Q: Show that the function f(x,y) =x² cos² y+ ysin² x+xe" , satisfies the 2 COS Lipschitz condition in…

A: