6. Are the following true or false, and prove your answers: (a) If A CR is bounded, then sup(A) € A (b) If A CR is bounded, then sup(A) is a limit point of A (c) If CCR is compact, then sup(C) exists and sup(C) € C

Q: 3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is…

A:

Q: Find the limit 2 ·lim t²-16 t-4 t³-64 3

A:

Q: a) Compute limits fox), if it exists, for the following cases X♡xo f:R R₁ x x1, x ²1 = =1 b.jf:…

A:

Q: d. Consider the following convex optimization problem min fo(x) s.t. x EN where O C R" is a convex…

A:

Q: 1. What can you say of a linear maping from P4 (R) to R4 such that the Null space is a line?

A: Let T:V to W be a linear transformation,  then  Null space ={ x in V : T(x)=0 } .

Q: 3. Find an open cover of (x:x>0} with no finite subcover.

A:

Q: 1) Evaluate the limit in each part if it exists Vx+2 -3 a) lim x-7

A: To evaluatelimx→7x+2-3x-7

Q: 5. Are the following true or false, and prove your answers: (a) If A is compact and B is bounded,…

A:

Q: From the given theorem I need the other part of the proof of (c) since the first one is solved. I…

A:

Q: Let A(0, π) υ (π, e 1| Find the limit point(s) of A. а. b. Is A an open set?

A: Given set is A = 0,π ∪ (π,e2]

Q: 12. A path is said to be closed if the function that generates it satisfies f(0) = f(1). Show that…

A:

Q: Show that each of the following functions is convex or strictly convex on the specified convex set:…

A:

Q: 3. Determine whether the following subsets of R are bounded above, bounded below, both or neither.…

A:

Q: Investigate the following func Mon por Local maximun and Local minimum point. 3) RCX, Y, 2 ) = x² +…

A:

Q: Consider the following sets: (c) C = (−1, 3) ∩ [−3, 1]. (d) D = (1, 2) ∪ [7, 8]. (f) F = {n 2 : n…

A:

Q: a) Compute limits. f(x), if it exists, for the follow Cases f³R DR₁ X 1X1₁ X6 ³1 Xo =1 b.) f: R^ →…

A: