Show that, with z = Rw, for some bounded w, || z(jw)|| w llw(jw)| ||R||. = sup means that -

Q: 73. Let z = f(x, y) .Show that g(x, y) fa (x, y)g(x, y) – f(x, y)g:(x, y) (g(x, y))² az and ax əz _…

A: Partial derivatives are functions with several variables. it is also the differential equation where…

Q: R (T) is bounded by its value at the origin i.e., IR, (t)l<Rxx (0) XX XX

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Q: 4. Let X₁, X2,..., XnEX and r> 0, for i = 1,2,3,...,n. Show that U=1 N (X) is bounded.

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Q: 2. Show that the following functions are convex by verifying the condition that V²f(x) 20 is…

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Q: How many distinct 5-letter strings can be created using the letters A, B, C, D, E if repetition is…

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Q: 2. Show that the following functions are convex by verifying the condition that V² f(x) 20 is…

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Q: 4. Prove that f(x, y, z) = 2 - 1 x² + y² is continuous in all its domain.

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Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: Let's assume that f(x)= r²+c* I c-16 g(x, a) = a* x² + ar Find a such that the following error is…

A: Given that where            That is  Also, given that

Q: [1+2p(x-1)+(x-1)² x≤1 x>1 [qx+p -) -) Find the values of q, in terms of p, for which fis continuous…

A: Given:f be a function defined by:a. To find the value of q in terms of&amp;nbsp;p, for which f is…

Q: AP1) Prove that f: E → R; x x² is uniformly continuous if E is bounded. AP2) Prove that f : R R; x x…

A: Definition: A function fx said to be uniformly continuous, if for every ε&gt;0, there exists δ&gt;0…

Q: Let F(x, y,z)=xi + yj+zk, f(x,y,z)=||F(x,y,z)||. Prove that: Vf" = nf"-²F F v(In f) =

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Q: 2. Let f be defined on an open interval (a, b) and assume that for some e e (a, b) we have f'(c) > 0…

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Q: f(z) = Im z is continuous 0 صواب ihi O

A: True

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: Find the absolute maximum and minimum values ​​of f (x, y) = x² + 2y²-x in the set D = {(x,y) ∈ R²…

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Q: Decide whether or not the real function In (eon 2) I+0, = (1) 1= 0, is continuous at r = 0.

A: The given function is fx=ln cos2x2x2     if  x≠0-1                if  x=0. Compute the limit…

Q: Clarify that f f :(0,1) →R defined by f(x): not uniformly continuous. =-

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Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

Q: of at (x, y, z) = (2, 3, 4). ay Let f(x, y, z) = (x + y)z. Evaluate

A: Given :fx,y,z = x+yz

Q: 5. Prove that |xy| = |x|-|y| for x, y eR.

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Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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Q: 1. Let f: [a,b] → R be a bounded function such that f(x) = 0 except at xo E (a,b).

A: A bounded function on a compact interval [a, b] is Riemann integrable if and only if it is…

Q: 5. Determine the vclue of c such that the function is continuous on (-o0,00 + flx) = 2x, x SC

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Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: Find its length over the given interval. (Round your answer to four decimal places.)

A: Length of a plane  curve: The length of a plane curve or the arc length of a curve r(t)=f(t) i^…

Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

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Q: f(x)=xmodx for all x  in R. Discuss the derivability of f(x) at x=0

A: Given:fx=xxwe have to find derivability of fx at x=0

Q: Letf (x, z) = 3x² – 12x + 3z² – In(z). Find the value of x* and z* where a min/max will occur. x*=2,…

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Q: Define f: Z x Z→ Z x Z by f((m, n)) = (3, 2n). Let A = {(n, 0): n ∈Z}. Fina f(A).

A: EXPLANATION : Given function  f:ℤ×ℤ→ℤ×ℤ defined by fm,n=(3,2n). given set A={(n,0):n∈ℤ}. putting the…

Q: Prove z = max (x,y) and z = min(x,y) are convex

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Q: For a derived varaible f : states → R is strictly decreasing if and only if for states q, q': → f(d)…

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Q: 3. Prove F (Vr)(A→ B) → (Vx)A → (Vx)B. ->

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Q: Check the convergence of the series Σ tan

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