i=12 let fi [a, b] →12 and: [c, d] → [a,b].діarecontinuous.ga) suppose I andProve that fog is integralbleble m [c, d].>b) Suppose I andare торо ниеgProve that fog is integral ble on [c, d].

let f:a,b→ℝ and g:c,d→a,b (a) suppose f and g are continuous . prove that f∘g is integrable on c,d…

Answered: i=1 let fi [a, b] →> IR and a) Suppose…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Can you help me with this question in my picture attached?
Suppose W is invarient under S:V\rightarrow{}V and T:V\rightarrow{}V. Show that W is also invariant under S+T and ST.
Determine if a funcbien fiR>R defined by 22 funcbron 25h (5tt)f Coりコ)キ100) 0, if (xy =C0,0) fCと)ニ continuous at c0,0).
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Please provide Handwritten answer
Recall the inner product (f,g) = S, f(x)g(x) dx defined on the vector space C([-]) of continuous (real-valued) functions f : [-, π] → R. Observe the following integral formulas, which are valid for natural numbers m, n > 1: • sin(ma) cos(nx) dx = 0 (0 cos(mx) cos(nx) dx = sin(mx) sin(nx) dx = ifm #n | if m=n 1. What do these formulas say about the angles between the vectors sin(n.), sin(m.), cos(n.) and cos(m.) in the space C([-])? What do say you about the lengths of these vectors? 2. Do you think these vectors form a basis for the space C([-,])? Why or why not?
Suppose R3 has the Euclidean inner product. Apply the Cauchy Schwarz inequality to the vectors u = (a, b) and v = (cos θ, sin θ) to show that | a cos θ + b sin θ |2 ≤a2 + b2. Note: Do not skip any step to arrive at the result, apply the Cauchy Schwarz inequality to arrive at the result (In the image the enunicoado is better seen)
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i=1 let fi [a, b] →> IR and a) Suppose of and g Prove that fog b) Suppose I and we is g до continuous. [c, d] → integralble are тороне → [9,5). m [c, d]. ▸ c [cd].