-1 2 -4 -5 -6 -7 -3 -2 -1 1 2 Above is the graph of f(x). List the critical numbers of f.

Q: Why must nCr always be less than or equal to nPr for any given n and r

A: Permutations and combinations are given.

Q: |1 0 A=[2 21 1 13 31 |A|=4 O |A|=1 O |Al=21 O |A|=0 O 900

A:

Q: 50 50 51 7. + 40 39 40 • () - €) (") - () () - () () 7 8. 4 10 9. 2 10 8 8. 8 8. 10. + 2 3 6.

A: We can solve the given problem using concept of fractions.

Q: 4.) Find the value(s) of k such that A is singular. 1 k 2 A = -2 -k 3 1 -4

A: The given matrix is                               A=  1  k    2-2  0 -k   3  1 -4 We have to find…

Q: Let X be a r.v. with p.d. f. ,x = 1,2,3, ... f(x): e.w. The value of a is: N I3

A:

Q: (2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

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Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: 3 = adj A. If |A| = - %3D

A:

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: NCx) = x² - 2x - 5 MQx) = 2x+3 N of M

A:

Q: 2 solve the following set of three equations by Gramer and by A XI-X22X3 = 1 2X1 - X3 = 2 X₁ + X₂ +…

A: Given the system of equations: x1-x2-2x3=12x1-x3=2x1+x2+x3=3 Solve using Cramer's rule.

Q: Let A = {x € Rx > 5 and x 15 and x 8 and x < 12

A: Given:- A=x∈R|x≥5 and x&lt;18 B=x∈R|x≥15 and x≤22 C=x∈R|x&gt;8 and x&lt;12

Q: Prove that: (5a + 6b|a, b = Z} = Z

A: To prove that .Concepts used:Consider two sets  and . To prove that , we first need to show and…

Q: (а b)с + (а - с)b + (с b)a 3 ve that v belongs to B.

A:

Q: AC Biff P(A) C P(B).

A:

Q: Use DeMoirve's Theorem to find: (1– iv3)2

A: We first try to express 1-i3 using polar form.r=12+(-3)2=1+3=4=2θ=tan-1yx=tan-1-31=tan-1-3=-π3So,…

Q: I. True or False. 1. N is closed under subtraction. 2. Z is closed under division. 3. Vx2 = -x if x…

A: A detailed solution is given below.     (As per our guidelines, We are supposed to answer only 3…

Q: Let a, b, n E Z. Prove: If a|n and b|n with gcd(a, b) = 1, then ab|n. (I

A:

Q: Example 68: (R, +,.) and (Q.+,.) are fieleds. (H.W)

A: I have proved the definition of field

Q: Find the rank- 1 approximation of

A:

Q: Evaluate (t – 4/i +t-')dt

A: Given : ∫t -4t + t-1dt

Q: 5. A. undefined B. 2 × 2 Consider (a) What is the size of QTP-¹? P= A. -1.5 B. -2 = [1 C. 2 × 4 D. 4…

A: Given: The matrix P=4611 and Q=22341-120 a) Find the size of the matrix QTP-1 b) Find the entry 2,1…

Q: 11! 1.) 5!x4!x3! 2.) Р(8, 5) 3.) Р(12, 4)

A: Our aim is to solve the following :  1) 11!/(5!*4!*3!) 2) 10!/7! 3) P(8,5) As per our guidelines, we…

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: Prove that gcd(a + b, a − b) = ged(2a, a − b) = ged(a + b, 2b).

A:

Q: What conditions, if any, must be set forth in order for a + b to be equal to n(A U B)?

A:

Q: 2 Let A = 1 (a11 + a22) A 2 Show by explicit calculation that A² and (a11a22-a12a21)I are equal.

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Q: Prove that OfVg.dr = ] (Vfx Vg) · N ds.

A:

Q: Prove the following statement: (VxR) (x 0 ⇒ (y R) (xy = 1))

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Q: . Show that sup{3 – 2 : n = 1,2, ...} = 3. %3D

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Q: -2 1 2 -1 1 -1 2. LetA= Then find A-1 if it exist. 1

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Q: DIVISION BYt (:) - {}> 81. Show that In %3D

A:

Q: 1. Find L-'[l/(p² + a?)²] by convolution.

A: Let 1p2+a22=1p2+a2p2+a2=1p2+a2p2+a2= FpGp      Then ft=gt=sinata

Q: (А - B) - С - (А -C)- (В - C)

A: Introduction :

Q: ). Find 1 |z-j|=2 Z

A:

Q: 6. El factor que va en el espacio ocupado por el símbolo "?" en la expresión 2-z (2-x)( ? ²+ = د ن ن…

A: The objective of the question is evaluate the missing part.