1. Let V = C[-n/2, 7/2] equipped with standard inner product. Show that (sin nr} U {cos mr}1 forms an orthogonal subset of V. (Hint use the identity: e" = cos(0) + i sin(0) for every 0 € R. %D %3D

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

A:

Q: Find div F and curl F if F(x, y, z) = 2eyi- 7 cos y j + 4 sin² z k. div F= curl F=

A:

Q: z = sin(6x) sin(5y) az az dy II

A:

Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

A:

Q: Disclaimer: Answers un-original (plagirized from external sites e.g. chegg) will be downvoted and…

A: Level curve: A curve formed by the set of points x, y where fx, y gives a constant value is called…

Q: e' [ S (5² +a²) 2 ] = t sinat 2a 7 Prove using Convolution

A:

Q: L L'FCE)]> F(4) = 4 sin #t

A: The solution is given as

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

A: The degree of a differential equation is the power of its highest derivatives.

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

A: The given function is: f(x)=xe-x ,      x>0

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

A:

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

A:

Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: F Sin(ncso)- Cscrsin o) , thes the valke of 10+4).

A:

Q: Find dy dx if sin(x + y) = tan(xy)

A:

Q: Prove that d/dz sin(z) = cos(z) using Cauchy-Riemann equations

A: Cauchy-Riemann Equation- If f(z)=u(x, y)+i v(x,  y) is analytic, then In particular, These…

Q: dw Find dx where w = cosz- cos 4x cos'4y + sin 4x sin 4y and z= 4x+ 4y. dw 口

A: lfirst put value of z and then expand cos term Now we get Zero whose derivative is zero

Q: Let f(x, y, z) = xre sin(x"yz) %3! 12 find dyözə³x at the point (3,0, 0) x²e*z sin(x²yz) Let f(r, y,…

A: First expanding the exponential function and sin as power series...