y show that = 0. . If z: x² + y² II

Q: Y Find det A 1SA - TAI = T.

A:

Q: Q5: a. Find * and for u - p=x+y+z ,and q = x+ y+ z, and r=x+y-z, at the point (x,y, 2) = (v3, 2,1).…

A: a)                          u=p-qq-r                             p= x+y+z;…

Q: What is t' (x) if t(x) = ? ez

A:

Q: Find the value of c such that S xe = 3.

A:

Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: If C is the z-axis from the origin to the point (0,0, 2), then So(3j – 3k) - d - dr |

A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

Q: b. Find y", given y = e¯" In x.

A:

Q: 2. Let j = Find the point on the line y x that is closest to j. %3D %3D 26

A:

Q: Find all values of n such that y = xn satisfies…

A:

Q: Vx e Z, 3y e R, y² = x

A:

Q: y z = x + show that : 0.

A:

Q: 04. Show that T = satisfies the equation T + Tyy = T³. %3D

A:

Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: Evaluate and simplify y'. In x where a is constant y In x + a

A: Given:   y=lnxlnx+a

Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

A:

Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

Q: Find Duf at P. f(x, y, z) = 4x'y°z?; P(1, – 2, 1); u = - 2. Duf

A: The objective of the question is evaluate the directional derivative at a given point.

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

A:

Q: Let y: (0, 3] → R?, y(t) = (t,?V³) and I := ran y. Sketch T and compute L(T) :!!

A:

Q: f({x, y))) for all c e R and all (x, y) E R?

A:

Q: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

A:

Q: b) y= In( see x)

A: Answer and explanation is given below..

Q: If y=e"Inx, show that x (1+x)=0. dr

A: Given: y=e−x.lnxShow  that:x2d2ydx2+dydx+e−x(1+x)=0

Q: Let z = e*y, where x = Vuv and y = . Find in terms of u and v.

A: Change the z in the terms of u and v and the differentiate.

Q: Z = X, + X, + at X1, X2. are NC

A: We are given,  X1, X2... are independent random variables with E Xn=mn  and N∈P0(λ). The set is…

Q: Q/ Let x~P(m) and let y = 5x , find the p.d.f of y

A:

Q: 3. Given z =, show that ху xy(zxx + Zyy) уз — х3 2 || x²y2

A: δwδt=δwδxδxδt+δwδyδyδt+δwδzδzδt       =ysin(z2).(-1)+xsin(z2).0+2xyzcos(z2)(2t)

Q: If Z = x.n. f (), then show that: x. Zx + y.Zy = z

A:

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

A:

Q: Let z = 3x*y, find Vz.

A:

Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

A:

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

A:

Q: xy Let z . Then: 4x2 – 5y? | az dz ду

A:

Q: Exl Let c R,Z) be usual toP s Pace and A-fcxy)ER/ x²+y²< 13 find A Ext CA), Ā , A°

A:

Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

A:

Q: a) If z= xy – xey/= , show that x * + y = xy+ z.

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

Q: Question dz If z(x, y) = x²y, x = ", and y = u'v², find

A:

Q: Evaluate G(x,y)dy , if Gx.y)=2xy ,x 5cost ,y 5sint ,0stsm/3.

A:

Q: ue of a and c are and

A:

Q: If z f(x,y) and z - y? = 6x?y°z? Find:器,需 and dz

A:

Q: Eliminate the parameter t: x = (v0cosa)t, y = (v0sina)t-16t2

A: *to find:- equation in the form of x &amp; y only, by eliminating the parameter t.

Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

A:

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.