0- V5 – x – V5+: -

Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

Q: 4v2 - 1 d)u =x²y" + xy + (x² – v²)y u" + (1.

A: Given that  LHS=u''+1-4v2-14x2u Simplify that to get,…

Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: x1, x2, x3...... x20000 iid U(2, 9), find approximation for 2X-20

A: Central Limit Theorem : If X1, X2 ..... Xn are iid random variable with mean μ and Variance σ2 then,…

Q: A 1 x る8 %3D 은 AB=C Find X+g?

A:

Q: Q.6 Show that: X-1 X+ y – 1(x-1y)= B(x,y)

A: In the given problem we have to show that                                 x-1x+y-1β(x-1,y)=β(x,y)

Q: f (x, y) x² + y² + 1

A:

Q: I'+yz² -2xyz = f(x*y+y*z+z*x)

A: Given:- x3+yz2-2xyz=fx4y+y4z+z4x

Q: Мaximize z 3 2х + у За + 4у < 36 6x + 2y < 36 Subject to Маximum is at y = VI VI ЛІ ЛІ II

A:

Q: y show that = 0. . If z: x² + y² II

A:

Q: | d²y +y³ = 0 dx² is not linear. صواب İhi

A: True

Q: Calculate the LOS of y = -x² + 4 LOS is x = a is b is c is

A:

Q: x-(1+iy) Q11: Express- in terms of z and z. (x-1)2+y2

A: Let z=x+iy and z bar =x-iy

Q: (1+v2)+i_ Z2 (1+2) (b) Show that -i 2

A:

Q: 4. y = vx +2 %3D x,for - 2 < x< 2 2, for x22 (x-1,for x< -2 5. y=

A: To sketch the graph of the given function and determine the domain and range.

Q: 1 y = V+ %3D x-1 x- 3 y = 4-x2

A:

Q: 2=Cメて+x -x2 Using Cramer's Rule メメt10n- 3xx=5 %3D

A: Solution using Cramer's rule is given as follows :

Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

A:

Q: 8. Let a2 + xy³ + 2x = 11. Find y"(x) at the point (1, 2). %3D

A:

Q: Y1 (t) = 2t – 3, y2(t) = t² + 1, y3 = 2t² – t, y4 = t² +t +1 %3D

A: We will find out the required solution.

Q: Suppose that a = xdy is a 1 form and Y(v1, v2, v3) = ((v1 – v3)² (v2 – v3)²) ædy what is "a ?

A: Given α=xdy-----(i)γ(v1,v2,v3)=((v1-v3)2,(v2-v3)2)---(ii) To find γ*α------(iii) from (ii) we…

Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

A:

Q: b. Min z = 4x1+ 2x2 s.t. 3x1 + x2 2 27 -X1 - X2 <21 X1 + 2x2 2 30 X1 and x2 are unrestricted .

A: Given: Minz=4x1+2x2s.t.3x1+x2≥27−x1−x2≤21x1+2x2≥30

Q: 3. 2. Z dydxdz 2=0 X=Z

A:

Q: iii) ä(t) – 9x(t) = 0, x(0) = 1, ±(0) = 0 -

A:

Q: 2t + 7 f(t) = t- 3 %3D h(n) = - 2n2-3n+1 %3D f(h(-1)) =

A: Here we have two functions f(t) and h(n), we want to find the value of f(h(—1)). To find f(h(—1)),…

Q: * 2.2 2x-1 + If y = Vx² – x then y' 3x2-x T O FO

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: f(x) =D V4- x2 1는 Jf %3D (-2,2) .1 (-00, –2) U (2, 0) 2 (-0, 2] U [2, c0) 3 [-2,2] .4

A:

Q: V1-x2 3. Evaluate S S /1-x²-y² dxdydz V1-x2-y2-z2

A: We will solve the following.

Q: V1-x² 1-x²-y² e-3(x²+y²+z²)² dz dydx a) Evaluate

A:

Q: Vị = 21 -+k V = 51 +j-k V, V2 1) |V2| 2) V V2

A: For any vector with coordinates, V=ai +bj+ck. The magnitude of vector V  is given by V=a2+b2+c2. Dot…

Q: .y² = 4x, x=0 to x= 4 %3D

A: Given  y2=4x  x=0x=4

Q: S2-3x', x>2 Vx -2, х <2 а) g(x)-

A: The given function is gx=2-3x3,   x&gt;2x-2,    x≤2. Sketch the graph of this function as shown…

Q: (j) z = y² – x² + 2x - (k) x² – y² + z² + 4.x + 2y = 3

A:

Q: px + qy=z-a √x² + y² + z²

A:

Q: 2. y(x) = C1sin2x + C2cos2x + 1; y) = 0 and y' ) = v2 C1 = C2

A:

Q: Q4 If z = x In(xy) a3 z a4z Find and əy²əx əx²əy²

A:

Q: a) Evaluate ²₁ √√1-x² √√1-x²-y²e-3(x²+y²+z²)² dz dydx

A: The given problem is to evaluate the given triple integral of Cartesian coordinates.

Q: dx Use a trig substitution to evaluate x³ Vx² x > 1. 1 6. -

A:

Q: = (y² – z² +3yz – 2x of the following is/a

A:

Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: 2x4 - 3x2 - 12x + 6 at 0 and -2 to deter f(x) = ero exists between the two values.

A: we have to evaluate the f(x)=2x4-3x2-12x+6 at x=0 and x=-2and to determine if the intermidiate value…

Q: A 3 X Y- X Y = 4xソーメニ2findr 3D2 and X"at X =1

A: Using definition of differentiation

Q: 8. f(x) = (2x³ + 9x)³ 9. s(t) = (5ª +2)(t² – 1)3/2 %3D

A:

Q: 1. V2 3y 8-x2-y2 رار 0 0 x2+3y2 dzdxdy

A: We have to evaluate the integral.     According to our guidelines we can solve only one question so…

Q: Y1 (x) = 8a + 2x; y2(x) = x In(bx); y3(x) = ca?.

A:

Q: Distanced is given by the distance formula.

A: Given points are P1x1,y1 and P2x2,y2. The distance between P1 and P2 is "d".

Q: 1- t2 (1 – 2xt + t2)3/2 (21+1)P(x)t' = %3D

A: Introduction The legendre polynomial denoted by Pnx. The solution of physical problems is the class…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.