2x (x-6) 3.) y = (x-3)3 required:a) yand y"

Q: 2. (i) Show that for a discrete dis.ribution B2> 1. (ii) Show that B2> B1

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Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: find in Euler's way 2x ! y(0.1) de y(0)=1 , h=0.05 y' = y -- y

A: The general form for Euler's method is given by yn=yn-1+hfxn-1,yn-1.

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

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Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

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Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: y If z = show that = 0. x + y?*

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Q: af 7. Compute and дхду a²f : f(x, y)=x'y² – sin 2 + xe" - əx' əy

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Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: az Find for z = x'y'eV

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Q: 2. W =I+xy- Z finds Wzz WZX NJ 3.

A: Given W = 1 + xy2 - z2

Q: and 3 point Gauss Quadrature 2 By using e sfim afe : 2 dx メ-2 い)S, dx Nx

A: The given problem is to estimate the integral using 2 point gauss quadrature rule and 3 point gauss…

Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: 9. If y = V-|x|, then Dr = %3D %3D

A: Df :  Domain of function f  The set of all input values where f defined

Q: Sm Vx dx

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Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

A: Given

Q: (1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

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Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

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Q: 7) If A = xz³i – 2x²yzj + 2yz*k, find VxA at the point (1,-1,1).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: In Exercise 5.8, we derived the fact that 4y1 Y2. 0< yı < 1,0 < y2 < 1, f(y1. y2) = 0. elsewhere.…

A: Compute the marginal density function of y1 using the formula: fy1=∫y2fy1,y2dy2 fy1=∫014y1y2dy2…

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: •1-i Evaluate 4z dz . J3i

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Q: H.w use Gramer Rule to Fird XIZ -2X-y+2 -3 %3D -2x43y- 221

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Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

A: We have to find grad(divV ) at (2,-1,0) where  V = (3x2y-z,xz3+y4,-2x3z2)

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: 6. Find the fized point of flx) [-,1] where', on fa = (동) x-(올)x3

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Q: 2. 2sin(хy) at x D 2, у3D Зя/4 3. z= In(x + 1) + y° at the point (0,3,9)

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: Suppose that z = f(x,y), find for 4 x²z* – 5yz³ + xy? - 3z? = x

A: Given: 4x2z4−5yz3+xy2−3z2=xz=f(x,y)∂z∂x=?

Q: 2. In OABCD, ZA = x, ZB = 2x +60. ZD = Draw a sketch to help you.

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Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: 2 I| ysin(xy)dydx Н.W.

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Q: 4. Show that 4= 3y'z' i+4x²:* j+6x°y°k is solenoidal.

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Q: Show that lm Casy -1 CoSy-1

A: