2. Let a = (a1,..., an) € R" and let f : R" →R be defined by f(x) = (a, x). Compute the following: a) Dif(x) b) Dzf(x) c) Vf(x)

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

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Q: f (x, y, z) = ln(x2 + z) + y2 exz. Fin

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Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

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Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

A: What is minimum and maximum Value: For a given set of numbers, the minimum value of the set is the…

Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: Let fn(x) = E s;(x) Y; be a linear smoother. Find a condition on the weights s;(x) so that fn(x) is…

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Q: Show that the function f (x, y)=(2 + x-y) / [1+ 2x ^ 2)+(3y ^ 2)] ∈R has a limit at (0,0).

A: I have provided a solution in step2.

Q: 2- Obtain the function x to minimize the following functional. J = | (xỉ + x3)dt St: X1 = -X2 ,…

A: Given functional J=∫01f(t)dt=∫01x12+x22dt------(1) here t is x(0)=C,   x(1)=D here C,D are fixed…

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

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Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

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Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: Define f : X → K by f(x) = x'(1), x € X. Again, the linear functional f is not continuous. By 6.4,…

A: Given: f:X→K by fx=x'1, x∈X To prove f is not continuous using the given corollary.

Q: Let Ximexp (A). Show i Sulficieny that T-ZXi is Statistics

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Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

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Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

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Q: 4. Show that the map K: [1, o) → [1, ∞0) defined by 1 t dt K(x) = 3 e 2 is a contraction in the norm…

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Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: Let f (x,y, z) = xyz2 + 1 and suppose that x(t) = 2 – t, y(t) = In(t), and z(t) = 3t. df Use the…

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Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: 3. If f(x, y,z)= In *yz +e tar's="), find f,,fy and f. . хуz

A: we have to find the partial derivative

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: If f:R⇒Rf:R⇒R is defined by f(x)=e−cosxsin(x)f(x)=e−cos⁡xsin⁡(x) for every x∈Rx∈R then…

A: The given function is: f(x)=e-cos x sin x To find the derivative first. f'(x)=ddxe-cos x sin x…

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: 10.Show that F(x, y) = (1 + xy)e*yi + (ev + x?e*y)j is conservative and find a function "f" such…

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Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: Find (if any) the relationship between the empty functions u(x,y) = xcos(t²) – ysin(t²), v(x, y) =…

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Q: 3. Prove by using the Squeeze Theorem, or otherwise: 1 t2 dt is continuous at 0. T sin t (a) (b) 1+…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

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Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: {x} € 1, Show that property (3) of a matroid implies: For any S e there exists y € S, such that S \…

A: Following is the definition of a matroid. A finite matroid M is a pair (E,?), where E is a finite…

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

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Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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