(xy + 1)dx + (x(x+ 4y – 2)dy = 0

Q: 1.11.9. Given a linearly independent set A in a vector space V, prove the following statements. (a)…

A:

Q: (2.3.15. Let X be a metric space. (a) Prove that SCX is bounded if and only if diam(S) < 0o.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1.4.10. Prove that the closed interval [0, 1] and the open interval (0,1) have the same cardinality…

A: (Schr¨oder-Bernstein theorem) :Let A and B be sets. Suppose there are injective functions f : A → B…

Q: Find the area of the shaded region. -h ( x ) = sqrt ( x + 14) -q (y)= sqrt ( y ) -16 -14 -12 -10 -8…

A: Ans= 40 squared units  For detail...go through the solution...I have done solution in detail

Q: Jesc'x dx

A:

Q: slane using GraphiI Hethod Max Z=3X+2k2 2X + Xe loo X+X+ 80 Onpt-

A: first we will draw the feasible region bounded by the constraints. then comparing the value of…

Q: 1.3.2. Let f: X → Y be a function, let B be a subset of Y, and let {B;}ie1 be a family of subsets of…

A: Let f:X→Y be a function, let B be a subset of Y and Bii∈I be a family of subsets of Y.  To prove…

Q: (2.9.13, Given continuous functions f, g: X F on a metric space X, prove the following statements.…

A: Note: (a) We say that f and g are continuous if and only if df(x),f(c)&lt;ε⇔dx,c&lt;δ The aim is to…

Q: 3.3.9. Given a normed space X, prove that the function p: X R defined by p(x) = ||x|| is continuous…

A:

Q: Prove or disprove. A closed and bounded subset of e' is compact.

A: PROVE OR DISPROVE :-  A closed and bounded subset of l1 is compact.

Q: 2. COsh(4x)dx

A: We have to solve given integration

Q: 1.8.7.) (a) Let an and b, be real or complex numbers. Show that if Yn and bn each converge, then E…

A: Let an and bn be real or complex number

Q: Given population parameters for two populations, population 1 has a mean of 800 and a standard…

A: Given that  Population 1  Mean (μ1) = 800 Standard deviation (σ1) = 40 Population 2 Mean (μ2) =…

Q: Full working plz, Thank you.

A: Suppose, I is the real image of an object O and let d be distance between the image and the…

Q: 4. Show that equivalent norms on a vector space X induce the same topology for X.

A:

Q: Material

A:

Q: 3.1.8. Show that if | | is a norm on the scalar field F, then there exists a positive number A> 0…

A: The solution is given below

Q: () Let X={1,2,3,4,55. Consider the Following topoloy on X R= {, X, $5}, {453, {2.3,5}, {2,3,453 ,…

A: Given that X={1,2,3,4,5} τ={ϕ,X,{5},{4,5},{2,3,5},{2,3,4,5},{1,4,5}} We know that the elements of…

Q: 6. %3D (5V2a + vb)(V32a 5.- – V4b) pnoie peƏ age

A:

Q: 2. Find the derivative of f(x) = -4x2 + 3x + 2 from first principles (i.e. the limit definition of a…

A:

Q: 1 V1 – x² dæ

A: To evaluate: ∫011-x2dx Solution: We know, ∫a2-x2dx=xa2-x22+a22sin-1(xa) +C     ..(1) We will use…

Q: Show that all open balls are bounded subsets of a metric space.

A: Solution: Let M=X,d be a metric space. For an arbitrary point a∈X, the open ball Bεa where ε&gt;0 is…

Q: 2.3.17 Let {xn}n€N be a sequence in a metric space X. Show that if InI, then either: (a) there…

A: Let xn be a sequence. Given that xn→x. We prove this as follows. If a) is not true then b) will be…

Q: .4.12 (a) Show that if X and Y are countable sets, then their union XUY Countable. (b) Prove that…

A: We prove following theorem by contradiction

Q: 3.7.4. Let M be a finite-dimensional subspace of a normed space X. Suppose that n E M and any E X,…

A: Given : M be any finite dimensional subspace of a normed space X. For any x∈M1 such that x = mx+cxy,…

Q: 2.9.11 Prove that every function f: Z→ F is continuous, where the metric on Z is the restriction of…

A:

Q: 2.4.4. Let X be a metric space. (a) Prove that X and Ø are simultaneously open and closed subsets of…

A: