8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

Q: Find y' at the point (7, 7) where z sin(z? – y*) + 46 = z² – 3. Türkçe: z sin(z² – y²) + 46 = z² – 3…

A: To find y' at (7, 7) Where  x*sin(x2 - y2) + 46 = x2 - 3....(1)

Q: Let f(x, y, z) = In(x² + 2) + y²e== – cos(2yz). Find fzyz- %3D

A: Given that: f(x, y, z)=ln(x2+z)+y2exz-cos(2yz)

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

A:

Q: dy sec (re ), y(In 4) = 3 / t dt

A:

Q: 8.If V=k r°, and V=4 when r=2 if dr/dt =2, find dV/dt ind th

A:

Q: Show that if sin z| is bounded along the straight line {(x, y): ax - By = 0}, then a = 0, i.e., z…

A: In this question, we have to prove z is in real R.  here we use the property of the hyperbolic…

Q: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

A:

Q: (c(2z+y), %3D ue of c in the joi F of W.

A:

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

A:

Q: Assume that after few w months, butterf lies papulace in looa is Calculated as: F(w)=12W+Cos (lbw)…

A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: Suppose that o(x, y) = e"-y and ø(ln 2, In 2) linear approximation to estimate o(ln 2 + 0.1, lIn 2 +…

A: Given that Φ(x,y) = ex-y and Φ(ln2,ln2)=1. Now by using the technique of linear approximation we…

Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

A:

Q: In(xy) cos(Tx + T) when x 2 and y = 1/2.- Find the tangent plane to f(x, y)

A: We have to find the equation of  tangent plane.

Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(r – 1) +2" – r has a critical number between…

A:

Q: 2 4 Differentiate cxprersion (use D for dy X y' w. respect tox

A: on diffrentiating with respect to x we get

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: Let Y1, Y2,..., Yn N(µ, 4), where is the unknown parameter. Find the MVUE for µ².

A: Fisher-Neyman factorization theorem: Suppose X1, X2, …, Xn is a random sample of size n taken from a…

Q: 12. Find the dicections at.which. the directronal.derivative af.f.(hg)..xSin xy.at.(,a).has.…

A:

Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

A:

Q: Let x,(t)-v(t)+sin(r), x,-vt) then x,(t)= xN-cosit) Select ones True, False

A:

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

A:

Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

A:

Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

A:

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

A:

Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

A:

Q: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: Find temperature in a rod with length L=2 and: Ut = 4uxx u(0,t) = 1,u(2, t) = 3 0 < x <1 u(x,0) =…

A:

Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

A:

Q: Use an integrating factor to solve the IVP y'+ytan x = cos x, with IC (x, , Yo) = (0,7), %3D and…

A:

Q: Let f(x, y) = 6e sin(7y) af af dy

A:

Q: Let f(x, y) = xcosy- y e*y. fxy at (1,0)is equal to:

A: For finding the Partial differentiation we need to take one variable constant and differentiate the…

Q: -2 X Given f(x,y,2) sin (z²y), show that fxyuy = fyxy %3D %3D

A: Given:- f(x, y, z) =e-2x sin(z2y)  To prove:- fxyy = fyxy

Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

A:

Q: Let f(x, y) = xcosy - ye*y. fry at (1,0)is equal to: -1

A: See the attachment

Q: 3. Let u =x² – 2xy+2y' with x = s´ · Int and y = 2s ·t° . au au and at Find as

A:

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: Put that: coshx- hel x+Jx=I/,.- cosh x= lml x+J xI/ メン」

A:

Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

A:

Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

A:

Q: is function oF x $ y xz + y In x = ze-sin (xy) D. Ausumo that z Find zx iF

A:

Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D

A:

Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·

A:

Q: sech 2t dt Evaluate 3, coth 2t

A:

Q: Show that if |sin z| is bounded along the straight line {(x, y) : ax - By = 0}, then a = 0, i.e.,…

A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D

A: 1. (a). To prove: ∫cschx=lnex-1ex+1+C Proof: We know that, sinhx=ex-e-x2 The left hand side can be…