(1) a) Using the Cauchy Integral formula (or otherwise) compute the following integrals. i) S 121=4 ez Cosπz dz ii) S z²+2Z Cashz 12-21-22-1 dz dz S Lii) √ (2²+9) (z+9) 121=4

Q: Assume that 2< a < 3 and1<b< 2. Prove that: 2 < a? - 2 < 8. VI

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Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: 3. Express using absolute value notation. a) x 3 b) -8 < xs8 c) xs-1or x21 d) x + ±5

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Write the following in interval notation {x €R: |x-1| < |x- 3|}- For example, an answer of), 4,…

A: Given,           x∈ℝ : x-1&lt;x-3

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

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Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: Find a pair of values (x, y) that serve as a counter-example for the statement that ⌈xy⌉ = ⌈x⌉⌈y⌉…

A: Let, x = 2.1 &amp; y = 2.5

Q: Show that V12 is irrational

A: A Rational Number is a number that can be written in terms of P/Q.  An irrational number can not be…

Q: Let 0 &lt; a &lt; b. Use the Mean Value Theorem to show that

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Q: frx) = Ty-x the domain of suppose What is

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Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Let a and b be non-negative real numbers with b+ 0 and p,q > 1 and+= 1, then a show that ab <+

A: Define a function y : [0,∞)→ℝ by yt=1q+tp-t1p, for every t∈ [0,∞). Now differentiating,…

Q: 8 Evaluate for (3x² -7x+4

A: We have to use the concept of derivatives

Q: Find the length of (3et − 3, 4et + 7) for 0 ≤ t ≤ 1

A: To find the length

Q: Q5. Given f(x) = v3x + 5, f: R → R where R is the set of real numbers. а) Find the domain and range…

A: (5) Given function is fx=3x+5 (a) We have to find the domain and range of fx=3x+5. Domain:- The…

Q: Provide answers in interval notation. 18) x2 – 5x s -4 x2_5x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find a pair of values (x, y) that serve as a counter-example for the statement that [ry] : |x||y for…

A: The ceiling function gives smallest integer that is greater than the number, that is, x is the…

Q: By using proporties of determinations,show that 0 a -b |-a 0 -c|= 0 b c

A:

Q: a. 2 |x – 4|| х-1 b. x? + 2х — 12 1 х+1

A: a.  (1, 2] and [3, (5+√17)/2]         b.  (-1-√13 , -1+√13)

Q: (d) The third quartile for X 提交答案| Tries 0/5 (e) the IQR for X 提交答案| Tries 0/5 (f) P(IX-216|> 41)

A: Given : Let X be a r.v X~N(216 , 18) Here ; μ=216 σ=18

Q: Let  Z∼N(0,1) . Then  P(Z>−0.73)  is     A.) 0.7673     B.) 0.4757     C.) 0.9418     D.) 0.6215

A: Given: Z~N (0,1)

Q: If the P-value is less than the a value, which one is correct? Reject Ho or fail to reject Ho Ans:

A: if the P-value is less than the α value ,than

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: 2. Determine all values of x - y when x and y are integers such that x = 360 + y².

A: The given equation is. x2=360+y2x2-y2=360x+yx-y=360 Since it is given that x and y are integers, so…

Q: Give an example of a function from A to B that is one-to-one. e) Give an example of a function from…

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Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i