10. If x, y and z are real numbers and x y°z10 > 0, which of the following must be positive? A x B C y'z D y!

Q: If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at…

A: At P1, 2, 3, A→=25ax+195ay+25az. As r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx, at the given point we…

Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

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Q: Which of the following is equivalent to the problem shown? 1 where 21 = rịcis01 and z2 = r2cis02

A: z1=r1cisθ1,  z2=r2cisθ2 Using the formula  cisθ=cosθ+isinθ

Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: aw and ar Q2) Find if as w = 2x + 4y - z, r+s X =r tan (s), y= sin (r - s), z=e**s.

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Q: if y= tan (cos(u)), u = cos )and t In(x2) dy then when x Ve is -8 5Ve 8 5Ve 4 5Ve -4 5/e

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Q: If 1 = T T (xyz – 3xy)a, + (zy² + 3x² )a, + xy a,] V(x? + y?) And B = r² a, + sin 0 aø Find |A x B|…

A: Given: B→=r2ar+sinθaϕ It is known that r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx. At P1, 2, 4, obtain…

Q: 13) W W A) reflection across y = 2 B) reflection across y = x C) reflection across y =-X D)…

A: To find the transformation rule here we check the axix of symmetry.

Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

Q: 52. If z = f (x, y), where x = r cos 0 and y = r sin 0, find a. Əz/Ər, b. дz/80, and c. d z/Ər d0.

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Q: 1. IF4=rzi-2y'?'j+xy's ,find ding at points (1.-1.1).

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Q: 4. a. Find zx + Zy: given that z(x, y) = tan(x3-3x?y2+2y4) V9-х2-у? b. If u then show that x ди дх…

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Q: What are the values of e and cz so that y(x) = c, sin(x) + czcos(x) will satisfy the conditions y(0)…

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Q: 2. Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a.…

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Q: If y = xsin then y is equal to = X" at x =

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Q: How many approximations for y = x sin(x²) must be made in order to obtain the zero of the equation…

A: Given that, y=x sinx2, x0=1.5. By Newton-Raphson method, xn+1=xn-fxnf'xn. Solve for n = 0.…

Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –…

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Q: Н.W 是, and , if ay Find ax Je az 11. f(x. y) = sin(y- x) 12. f(x. y) = tan %3D %3D por

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Q: 3. Find an equation of the form y = ab* +c sin x) that fits the data below x01 2 3 y 4 11| 16 29 A.…

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Q: 10 Suppose z = x + 2i and u=3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Given z=x+2i and u=3+yi

Q: Solve the following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 2. y"" – 3y" + 3y' – y =…

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Q: EX Use Euler's method ( modified) to approx; mat e y' = x+y for yC1) = 1; h=o.1,13X<z withe aecuracy…

A: We Use here Euler's Modified Method to find the solution.

Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: If y = tanh"( k /x) and vx (1 - 9x) y'=A Then A =... Answer:

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Q: What are the conditions on A, B and C for an ODE of the form Ay'' + By' + Cy = 0 to have solutions…

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Q: If u = sin® 3 - x 2 find Ou Əx Ou and ह Hence show that 2 Ou 1 y x 3 –x dy Ou = 0

A: Given u=sin-13-xy2

Q: 28. IfI:zxzr = 0, ris a. positive b. negative с. zero d. impossible to determine from the…

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

Q: In Exercises 5–12, find and sketch the domain for each function

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Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: Let y(x) be the solution for the DE y+ytan(x) + sin(x) 0 If y(0) = In 2, then at x= the value of y…

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Q: U Sin/X-Y Show that Itanu. 2. LL

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Q: - Given y= ela's -x²-In'r, what is y'?

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Q: 3. If X' such that the second solution is of the form X, = te+Be, then B = Select one: O a. Ob.

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3…

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Q: 13. If byy and b, YX XY y are both positive, then : (A) (1/byx) YX + (1/bxy) < (2/r) XY)

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Q: ,3 Let w = x'y cos(2z). Find the following. dw (a) (x, y, z) = (b) (x, y, z) = ду (c) (x, y, z) = dz

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Q: Find u(x, t) which solves the problem Utt = 9urr -00 < x < o0, - 0 <t <3; 1 u(x, 0) = 1+ x2 Ut(x, 0)…

A: D'Alembert Solution;    u(x,t)=ux,t=12f(x+ct)+f(x-ct)+12c∫x-ctx+ctg(ξ)dξ where u(x,0)=f(x),…

Q: Suppose z = x + 2i and u = 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Given that z=x+2i and u=3+yi where x,y∈R. Now our aim is to find the smallest value for x for which…

Q: aw and ar dw O Find if as

A: In this question, the concept of the derivative is applied. Derivative  A a derivative is used to…

Q: If So I; (x² + y²)sin(x)dædy = fo ,2 Sa(x² + y² ) sin(x) dydx then a, b are

A: if  ∫01∫y1x2+y2sinx dx dy =∫01∫abx2+y2sinx dy dx then find the value of a ,b

Q: 10. z = x² sin y, x = s²t, y = st

A: 10. Given,   z=x2sin(y), x=s2t,  y=st.

Q: 6., Given that= 1' + sy = ) and that y = 1 dr (a) show that for values of r close to 0, 1 when = 0,…

A: Let y(x) is a function. Then the expansion of Taylor series of the function y(x) at the point x=a…

Q: in a paragraph proof please

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Q: If So S, (x² + y² ) sin(x)dxdy= f L (2²² + y?) sin(x) dydæ a , then a, b are

A: Solution is below.

Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.