Remind yourself what () means. For this class, we will use the convention that () = 0 if n < k or if k < 0. (a) Prove that A() - ("). (b) Prove that A(") = ()- (c) Make an educated guess about A)- (d) Write 3n2 + 4n – 1 as a combination of (), (). and (). In other words, find a, b, and c so that 3n° + An – 1= a() + +(;) +C)-

Q: [(r* - 1) (4 – x* )ax

A:

Q: In(x²) = 2 ln(x) for all x True O False

A: ln(x^2) =2ln(x) for all x

Q: Let M(x) = V3x – 6 and N(x) 2 Find the following: 2 - c) (N o M)(5) d) (No M)(홍) e) (No M)()

A:

Q: 1a) suppose that f is defined recursively by: f(0) = 5 and f(n+1)= 2fn + 5. Find f (1) f(2) f(3)…

A:

Q: 5) Evaluate the expressions below if K(s) = 3s² - s+6. a) K(s+2) b) K(s) +2

A:

Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

Q: finD 1) 2) g(s (x) a) p(x) x?-2x+2 b.) g4)==3x t. %3D cl.) s(x) = x-1 4) Cx))

A: Given that px=x2−2x+2, qx=3x+1, rx=x and sx=x−1. 1 We have to find the prx. prx=pxUse…

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: Which of the following is equivalent to - (Vx (P(x)VQ (x?),

A: we will use demorgan law here 1)   ∼(P∧Q)=(∼P)∨(∼Q) 2)  ∼(P∨Q)=(∼P)∧(∼Q)

Q: 3. Invent two interesting and original positive integers a and b. Let f(x) = ax +3. (a) (b) What is…

A: Given function is fx=ax+3. To find:  a  f10   (b). A number x such that fx=b Solution: Given…

Q: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: Given is a expression  1215-x&gt;24-2x2. It is required to prove the given expression for all…

Q: 2 Show that for n>o Ê i=0 (-1) ( ^^ ) = 0

A: We have to show

Q: If P(A) = P(B) = P(AB), show that P(AB + AB) = 0 [AB = An B]. %3D

A:

Q: Show that /(-1)-7(1) but there is Let f(x) 1 Show that /(-1) (1) but there is no number e in (-1, 1)…

A:

Q: Suppose that an = 4" a₁x² + 2a₂x³ + 3a3x4 + 4a4x³. as 00 (i) f(n)x+2 n=0 00 (ii) Σ g(n)x¹+1 n=1 00…

A:

Q: α Let V₁ = {(₁)|a € R}. V₁ with standard V4 operations will fail both axiom "close under addition"…

A: Let A be a set and ∘ binary operation on A then 1. We say A is closed under the binary operation ∘…

Q: 1. (a) 2 Let = (1, 0, -2) and = (-4, 2, 3). Find a real number x such that (ট' –æè) ⊥ à. (b)-1 (c) 3…

A: Let .To find a real number  such that .

Q: By using Caushy Rieman prove that (2) and (3) (2) 4c2) = (3) prove That (3)- 3.

A:

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: Now we assume that P(r) is true, that is, r can be written as a sum of 3s and 5s, for any cases,…

A: We are given a statement and its proof. We need to answer two questions about the proof. More…

Q: Suppose L(x) = "x is a llama" and E(x) = "x is an emperor." Do the following to statements mean the…

A: Consider the given information:

Q: Let p denote 3x E Z such that P(x)" and q denote dx E R such that P(x)". Ğive a simple definition…

A:

Q: Which of the following statement is always false? (a) For all integer x, [x] = [-x] (b) For all odd…

A:

Q: 2. Find (w + 1)(w-w+1).

A:

Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

A:

Q: Prove that (+¹)=()+(²1).

A:

Q: (b) Prove that 32n²+1, for n ≥ 1.

A: The given inequality is 3n≥2n2+1, for n≥1. We have to prove this inequality.

Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

A:

Q: .

A: Given, The matrix,

Q: (9) Let P, Q, R be (a) (¬P VQ) (b) (P mathematical statements. Negate the following statements.…

A: