Let f lx):3x,9J=xland hlx): Ne Express each function below as a Composition of any twO of the above functions. A aI(x): V3x bi Klx):3L

Q: If f(x, y) = xsec²2y + ycosec²2x + 2xy then show that, drdy dydx

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Q: Let f(z) = x² +iy² where z and y are the real and imaginary parts, respectively of z and C is a…

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Q: Let f (2) be an analytic function, which is represented by f (2) = u (x, y) + iv (x, y) where z = x…

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Q: let (X; Z) v it piece wise comnected ?

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Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: • The Doman of f(x) = 4-Vx is 1. (2, co) 2. [-2, c0) 3. [2, 0) 4. [-2,2]

A: The domain is the set of all values of x for which the value of function f(x) exists.   For f(x)=4-x…

Q: Prove the following equation by showing the function is square-integrable on the real line, ||r±…

A: As the function is square-integrable we will construct a Hilbert space having inner-product…

Q: Let x, y be real numbers such that xy=1x and x≠y. Prove that x^2+y^2≥2\sqrt{2}|x−y|.

A: Given: xy=1x,x≠y To find: x2+y2≥22x-y

Q: For the scalar function f, div(grad f) is equal to

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Q: For the function f(x,y,z) = In (5x + 4y + 9z), find f,, fy, and f,.

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Q: If f(x,y)=x²y+y sin x, Prove that дхду дудх

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Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: Let R represent Winnebago county in Illinois, and let f(x, y) represent the total annual snowfall at…

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Q: Let x be the r.v Such that ECx)=D2 ECx)=2a %3D [2+Qx}?) =2a3 %3D Findthe Value of a

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Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

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Q: Let z = f(x, y) = 4x² + 2xy + By, Step 1 of 4: Evaluate f(3, 1).

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Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: Let f(u,v)=u2−v2, u=xy+z, and v=2x+y2 . Find ∂f/∂z in terms of x, y, and z

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Q: Let R represent Winnebago county in Illinois, and let f(x, y) represent the total annual snowfall at…

A: Consider the given: R represent Winnebago country in illinois.fx,y represent the total annual…

Q: Given a function f(x,y,z) = 5x² In (7y + 3z). Find the domain of the function. %3D o {(xy,z) |z >…

A: Use logarithms definition to choose the correct answer.

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

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Q: suppore that f(x.v,Z) = x*y +x2 and x cu,v) = sincu)t(os (u) Y(u, v) = Sincu) - (oslW find of oflav…

A: Given: f(x,y,z)=x2y+xzx(u,v)=sinu+cosuy(u,v)=sinu-cosu To determine: ∂f∂u,∂f∂v

Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: Let f:R-R defined by f(x) =x² , then f ( x) is bijective صواب ihi

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Q: Let f(z) = x? + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

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Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: prove that 16 x (I+x) dx 306

A: The product rule of integration states that∫fxgxdx=fx∫gxdx-∫f'x∫gxdxdx.

Q: Determine the voctor ficld of F. F(x, y) = 12i - 4j

A: We have to draw vector field of given vector.

Q: Let f (2) = x² + iywhere x and y are the real and imaginary parts, respectively of z and C is a…

A: The given problem is to find the value of Re[f(z2)], where given z2 = 8+7i and function f(z)=x2+iy2…

Q: Consider the function g : ZxZ → Z × Z defined by g(x, y) = (4xy, 9x + 5y). (a) Is g injective? (b)…

A: (a) we see (5, 0) and (0, 9) are different elements in ZxZ.      But, g(5, 0) = (4.5.0, 9.5+5.0) =…

Q: . Evaluate F dr, where F(x, y) = ryi+z'y²j, and C is given by r(t) = ti+tj. 0sts1.

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Q: Consider the fiunction f(x,y) = x² + xy – 5x - y +1. Then:

A: f(x,y)=x2+xy-5x-y+1

Q: Let f:R-R defined by f(x) =x² , then f(x) is bijective صواب ihi

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Q: Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property…

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Q: Let f (x) = vr +2² + 2 , ro = 1, h = 0.5, r1 using the Three-Point formulas to approximate f(1) (1);…

A: Given: The given fx=x3+x2+2, x0=1,h=0.5,x1=1.5 and x2=2

Q: Determine whether the functions is a bijection from R to R. f (x) = (x + 1)/(x + 2) +

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Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: Let r (t)= - The x component of r' (-1) =

A: r'(t)=<2t,3,5> r'(-1)=<-2,3,5>

Q: If f(x, y) 3D х'у? — 2x'y + 3х, find (а) f.(x, у) and f,(х, у), (b) f:(2 , –1) and f;(2 , –1)

A: To find partial derivatives of f(x,y) = x3y2 - 2x2y + 3x To find :- (a)fx(x,y) and fy(x,y)…

Q: Given a function f(x,y,z) = 6x² In (8y + 9z). Find the domain of th function. o { (xy,z) | z >…

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Q: Find all values of x so that v · v = 1, where

A: Given vector, v=12-12x That is v=12i-12j+xk

Q: For the function f(x,y,z) = In (5x + 7y+ 9z), find fx, fy, and fz.

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Q: Let f: X Y and suppose S, {A;}ieI C P(X) and T, {B;}jeJ c P(Y). Show that cn. iel (i) f

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Q: Let w = f(u), where u = x g(y), show that w,xx = f" (x g(y)). g²(y). %3D

A: Let w=f(u), where  u=x g(y). So using the chain rule, differentiating with respect to x, we get…

Q: Let F(x, y) = <3x?y3 + y", 3x°y² + y^ + 4xy³,. %3D Evaluate F. dr where C is the line segment from…

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Q: Let F = (x + y) exp(x), x = ln(u), and y = v. Find Your answer should be in terms of , y, U, and v.…

A: We have to find partial derivative

Q: Consider the function f(x) = VI on some closed interval and by applying the Mean %3D Value Theorem,…

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Q: ) Use Stoke's theorem to evaluate f f.dr in the counterclockwise direction when viewed from the…

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.