84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

Q: E [X - E ( X)]2 is Select one: O a. V( X) O b. E ( X) O c.E ( X2) O d. S. D(X)

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Q: . What is the coefficient of a" in (2 – x)"?

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Q: The Lucas numbers L(n) have almost the same definition as the Fibonacci numbers: if n = 1 if n = 2…

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Q: Let > 0 and 6 > 0 be real numbers that satisfy e' (1+a+²) = eª (1+b+ 2 ) eb Prove or disprove that a…

A: Its given that a>0 and b>0. We have to prove or disprove that eb1+a+a22=ea1+b+b22 is satisfied…

Q: e the exact value of the function for the given x-value without using a calculator. ( ) f(x) = f(x)…

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Q: 7. Given that , -f() = 15, which of the following must be true? O-35, f (P) dp = 15 O-3 f (p) dp =…

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Q: C. Name two angles that are supplements of zT Q O ZS and LT O LS and Q O ZRand zQ OZR and 2S

A: Suppliments means the sum of two angles should be 180°. When a line cuts the two parallel lines than…

Q: 49. Prove that x +> 2 (x1/2 – x-1/2)2. 2 for all x > 0. Hint: Consider

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Q: 21.) lim √9th -3 h+o h

A: The given limit limn→09+n-3n

Q: 6. If x#0, which of the followi A x2 B +3 C) x4 D xS

A: We will solve the following

Q: 3. Prove or disprove the given statement. (a) If x e R, and x + 0, then 2x > x. (b) If n e Z*, then…

A: Given: (a) If x∈R, and x≠0,then 2x>x (b) If n∈Z+, then 2n-1>0

Q: X = к (x+21) 47 M

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Q: 8.5.2 Example B Calculate x given that it satisfies the relation 3" = 5x. (8.193) This latter…

A: We have to explain the given points .

Q: If Xo and X, are two numbers with Xo F(X1) O B. F(XO) = F(X1) O C. None of the above O D. F(X0) <…

A: It depends on the conditions; If F is a increasing function then option D is correct. If F is…

Q: iid Let X1,, Xn N(u, o). Find 2(n 3) (X2+ + X(n-2)) + 16 X(n-1) +Xn if,E(i) 16 17(n-2) 16(n-3) 4…

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Q: The Maclaurin series for f(x) = x'e2) ts: -2)*x**2 (b) (a) (e) None kl k!

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Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

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Q: c. x[n] = e and d[n-5]

A: As per the question we have two discrete signals : e-n² and  δ[n-5] And we have to find the…

Q: 42. Let e = 1+ 1/1! + 1/2! + 1/3! + Show that if k is a positive integer, then kle is not an…

A: Given , e=1+11!+12!+13!+....we need to prove if k is a positive integerthen k!e is not an integer

Q: Suppose P(A) = 0.4 and P(B) and B, show that 0.1 ≤ P(An B) ≤ 0.4. = 0.7. With no other assumptions…

A: We have given thatP(A) = 0.4P(B) = 0.7We have to show that0.1 ≤ P(AB) ≤ 0.4

Q: anel g(x)= |- Vã , Fino × =(Xつ f え a- fog and gof b- thei range and domain of fo9 3 9of.

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Q: 1009 1010 R= E (2k) =2+4 +6+ ... +2018 and S= 2 (2k- 1) = 1+3+5+...+ 2019. What is the value of R-…

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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: How far will a wheel with radius 14cm travel in TWO revolutions? Give your answer to the nearest…

A: To find the distance covered by the wheel in two revolutions

Q: b) Evaluate UTM L{t*e- 6(t-2)}. TM

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Q: Given that g(x)=3x² - 5x+6, find each of the following. a) g(0) b) g(-2) c) g(2) d) g(-x) e) g(1-t)

A: Given g(x)=3x2-5x+6 We are required to finda. g(0)b. g(-2)c. g(2)d. g(-x)e. g(1-t)

Q: If Xo and X, are two numbers with Xo < X, then the true one is

A: Answer:-  Option D is the correct answer.

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…

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Q: 2 8. 10 Which function is represented by the graph? A) f(x) = 2x + 6 B) f(x) = -2x + 6 C) D)

A: We have to check the graph

Q: Find the constant C such that * x3 – 3x + 8 < C, where x e [0, 3] | 18 O 23 14 17 O 26

A: We have to find c

Q: Let X~ N(1,4). What is E(X²)?

A: Here, it is given that X~N(1,4) that is X follows Normal distribution with mean μ=1 and variance…

Q: 4 This is Discreet math please answer questions with proper formatting for proofs

A: Given that (a)Given two positive integers x and c, if  x+ c &lt; 5, then x5 =x+c5 and (b)given two…

Q: Q5: Suppose B is real. Show that le2ßt - 1|< 27|B| , 2 πβί

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Q: Let f(x)= 2x ; OCxCI, Find E(3X+6) 3 4 8. 6.

A: In question, We have given pdf of X. Then we'll find the value of E(3X+6). The solution is below,