1. (a) Consider the set S {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and Max(S). nex}. 2n :ne N 1 3n +1 (b) Let B = 1 i. Prove that inf B 2 ii. Show sup B = 3 (c) If r, y ER such that r> 0 and y> 0. Using the fact that,rE R, a2 2 0, prove each of the following. 1 xyS(x+y). i. Vry 2 1 ii. ry <; (x² + y*).

Q: Determine. '{F}. 4s2 + 3 sF(s) – SF(s) – 2F(s) = - s + 4s

A: Rewrite the given equation.

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

A:

Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

A:

Q: Suppose that x is N(15,4). Find the P(X>11).

A: The random variable X follows normal distribution. The population mean is 15. The population…

Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

A:

Q: P(|X|>1.3)

A: In statistics, the t-distribution is a probability distribution that arises in hypothesis testing…

Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

A:

Q: P(x) = 1. Let x! and let H=10, Find P(9)

A: To find: P(9)

Q: Q2. P(A) = 0.42, P(B|A) = 0.66 and P(B|A’) = 0.25. Find the following – P(A’), P(B’|A), P(B’|A’),…

A: We have given information, P(A)=0.42 PB|A=0.66 P(B|A')=0.25

Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

A:

Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: n² -1) 2n³ + 1

A: ∑n=1∞ -1nn22n3+1 use the alternating series test an=n22n3+1 an is positive and monotone decreasing…

Q: verify that (AT )T = A

A:

Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

A:

Q: Show that E(r(r + 1) =- n(n + 1)(n + 2), n E N.

A: We have to show that ∑r=1n(r(r+1))=13n(n+1)(n+2)           ∀n∈ℕ

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

A:

Q: (4b) Let n E Z. Prove that if n is even, then n² + n + 2 is even.

A:

Q: Supppose that X ~ N (2; 3). Find P (1 &lt; X &lt; 4).

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.