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kot 1: (0, l) → R he a bounded lunction and on he acquence n OI). Proue thiat there is a sub kot 1: (0, l) → R he a bounded lunction and on he acquence n OI). Proue thiat there is a sub
the set A ⊆ L^2 by A = { {xn} ∈ L^ 2 : X∞ n=0 (1 + n)|xn| 2 ≤ 1 } Prove A is totally bounded, and compact.
the set A ⊆ L^2 by A = { {xn} ∈ L^ 2 : X∞ n=0 (1 + n)|xn| 2 ≤ 1 } Prove A is totally bounded, and compact.
Sub-problem 2. Recall the eztreme value theorem: If g(ax) is continuous on (0, 1], then g attains its marimum. In particular it is BOUNDED. L.e. there is a number M20 such that 1. Find a number M...
Sub-problem 2. Recall the eztreme value theorem: If g(ax) is continuous on (0, 1], then g attains its marimum. In particular it is BOUNDED. L.e. there is a number M20 such that 1. Find a number M so that lg(a)l s M, where g(x)x(1-) (Hint: marimize g 8. Provide an erample of a function that is NOT continuous on [0, 1] but IS bounded. 3. Provide an ezample of a function that is NOT continuous on [0, 1] and that...
A. 0≤P(Oi)≤10≤P(Oi)≤1 for each i B. P(Oi)≤0P(Oi)≤0 C. P(Oi)=1+P(OCi)P(Oi)=1+P(OiC) D. P(Oi)≥1P(Oi)≥1 If an experiment consists of...
A. 0≤P(Oi)≤10≤P(Oi)≤1 for each i B. P(Oi)≤0P(Oi)≤0 C. P(Oi)=1+P(OCi)P(Oi)=1+P(OiC) D. P(Oi)≥1P(Oi)≥1 If an experiment consists of five outcomes with P(O1)=0.10P(O1)=0.10, P(O2)=0.20P(O2)=0.20, P(O3)=0.30P(O3)=0.30, P(O4)=0.40P(O4)=0.40, then P(O5)P(O5) is: A. 0.50 B. 1 C. 0 D. 0.25
Please give me the correct solution. Consider the bounded function f : [0, 1] + R...
Please give me the correct solution.
Consider the bounded function f : [0, 1] + R defined on the closed interval [0, 1] by 0 т f(x) = { 15 if x is irrational, if x is rational with r= – where m <n are positive integers with no common factor (other than 1), if x = 0 or x = 1. n 1 (b) Is the function f integrable on [0, 1]? If your answer is "yes," then prove...
s h) for all z c l e Sub-problem 3. Recall monotonicity of integration: If h() S [-1, 1], then This just says that integruls preserve inequalities 1. Explain why this is true graphically 2·Let...
s h) for all z c l e Sub-problem 3. Recall monotonicity of integration: If h() S [-1, 1], then This just says that integruls preserve inequalities 1. Explain why this is true graphically 2·Let g be continuous on [0,1]. Use the previous item, and the fact that to show that 3. Use the first two items to show that if g is bounded, say Ig(r)l s M for z [0, 1], then first two derivatives are continos on is...
oi o 2. Find the area of the part of the paraboloidty that is cut off by the plane -4 3. Find volume of the solid in the first octant bounded by y 2r and the plane r-4 3. Find volume of th...
oi o 2. Find the area of the part of the paraboloidty that is cut off by the plane -4 3. Find volume of the solid in the first octant bounded by y 2r and the plane r-4 3. Find volume of the solid in the first octant bounded by y= 2x, and 4. Find the volume of the solid bounded above by the spherex2+y+ 4. Find the volume of the solid bounded above by the sphere+y?+ 2 9, below...
what is the electric field at the centre (r-0) of a hemisphere bounded by r-a, 0...
what is the electric field at the centre (r-0) of a hemisphere bounded by r-a, 0 < θ 〈 π/2 and 0 < φ 2π, that carries a uniform volumetric charge density ρ,-3φ(구)? (The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) 1.
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R. 9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u...
9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R.
9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R.
10. Use Duhamel's principle to find a bounded solution to utAu+ f(r,t), 0<r< R, t 0, u(R,t) 0, t>0, u(r,0) 0, 0sr <R. 10. Use Duhamel's principle to find a bounded soluti...
10. Use Duhamel's principle to find a bounded solution to utAu+ f(r,t), 0<r< R, t 0, u(R,t) 0, t>0, u(r,0) 0, 0sr <R.
10. Use Duhamel's principle to find a bounded solution to utAu+ f(r,t), 0
Sub-problem 2. Recall the eztreme value theorem: If g(ax) is continuous on (0, 1], then g attains its marimum. In particular it is BOUNDED. L.e. there is a number M20 such that 1. Find a number M so that lg(a)l s M, where g(x)x(1-) (Hint: marimize g 8. Provide an erample of a function that is NOT continuous on [0, 1] but IS bounded. 3. Provide an ezample of a function that is NOT continuous on [0, 1] and that...
Please give me the correct solution.
Consider the bounded function f : [0, 1] + R defined on the closed interval [0, 1] by 0 т f(x) = { 15 if x is irrational, if x is rational with r= – where m <n are positive integers with no common factor (other than 1), if x = 0 or x = 1. n 1 (b) Is the function f integrable on [0, 1]? If your answer is "yes," then prove...
s h) for all z c l e Sub-problem 3. Recall monotonicity of integration: If h() S [-1, 1], then This just says that integruls preserve inequalities 1. Explain why this is true graphically 2·Let g be continuous on [0,1]. Use the previous item, and the fact that to show that 3. Use the first two items to show that if g is bounded, say Ig(r)l s M for z [0, 1], then first two derivatives are continos on is...
oi o 2. Find the area of the part of the paraboloidty that is cut off by the plane -4 3. Find volume of the solid in the first octant bounded by y 2r and the plane r-4 3. Find volume of the solid in the first octant bounded by y= 2x, and 4. Find the volume of the solid bounded above by the spherex2+y+ 4. Find the volume of the solid bounded above by the sphere+y?+ 2 9, below...
what is the electric field at the centre (r-0) of a hemisphere bounded by r-a, 0 < θ 〈 π/2 and 0 < φ 2π, that carries a uniform volumetric charge density ρ,-3φ(구)? (The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) 1.
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R.
9. Find a bounded solution to the exterior boundary value problem Δυ = 0, r>R, u = 1 + 2 sin θ on r-R.
10. Use Duhamel's principle to find a bounded solution to utAu+ f(r,t), 0<r< R, t 0, u(R,t) 0, t>0, u(r,0) 0, 0sr <R.
10. Use Duhamel's principle to find a bounded solution to utAu+ f(r,t), 0
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