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Q: Can you prove that it is injective by contrapositive? Also, how is f surjective when y exists in R?

A: Different equivalent definitions can be given for injectivity. The function f:A→B is injective if…

Q: B) Let f:R - R be defined by. 3 if x rational number. f(x) = if x irrational number !3! Show that f…

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Q: O If fCos,y)=xty-xy%,find Joc-1,y-2. DIf 2=ea>c+ ky oflexx-by), Prove thet baz + ag = 2abz.

A: 1.Given function is fx,y=x3y-xy3. We have to find 1fx+1fy1,2

Q: het fncx) = 1 + 1JCa 10 Evaluate [faces doc @ Find facad face) and face) Ⓒ find lion faces and f'cor…

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Q: Prove η ΣΙΑ - ΣΡΑ) η;=1 Hint : use Chebyshev's inequality PO when A are independent

A: To prove that when are independent, we can utilize Chebyshev's inequality.Let's define , where is…

Q: 9) 444 (11) Evaluate the following integral; A) 4 Injx-21-In/x+3/+C C) 4 In/x-31-In/x+2)+C B)…

A: Here we can use method of partial fractions to find the required integral. We also need the…

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Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

Q: b) Evaluate the intergral. Show (with your work) that it is Cunvergent and give its Value or that it…

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Q: Give the reason(s) for each step needed to show that the following argument is valid. [p^(p→q)^ (s v…

A: We have to write the reason for the steps.

Q: Prove that (23-1a,b)* = {2}-1/a})(27-1) j=1 for all real numbers a₁,..., an and b₁,..., bn. i=1

A: The detailed process is described in step 2.

Q: 2 is a counterexample of vxay(x = 1/y), where the domain for all variables consists of all integers.…

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Q: x + 1 is not f uu ction 1] True 2] Fulse

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Q: 4. a) Prove that A i) V=I I+A 1+A ¡¡) fx+nh = Σx=0 (7) 4¹ fx.

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Q: on Give an crample of a dis continous bijection fo[at] = [1,2]

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Q: Calculete Je by integlat: to 12+-3)dt Letter S, ot number 5 -st thenz 3.

A: Calculate integration by part in the following way:

Q: Aşağıdaki önermelerden hangisi yanlış önermedir? A) (pq) → r = p< (q + r) B) (pq) → r = p → (q→r) C)…

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Q: Use a proof by contradiction to prome that integer ond 3n+z then

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Q: (10) LE (P

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Q: Psuppose that fandg are Funcnans. severalvaiverof ECA), F()19g(x). and g'ex) aregiven below. Use…

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Q: L Idempotent Law 2 Double negation law b.) p (qVr) E-pV (qVr) 3. Associative law c.) (pv q)A [~…

A: From the given we have to match pair of law and the logical statement.

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: What is true about the function *) - as *-* ? A) B)(x)→0 from below OC) f(x) is undefined OD)x)→…

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Q: Let F) be a differentiuble func Hen Such that Then g/2)= AS 912)= the equaben of Hhe fagat ine to…

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Q: O Find the any le Ô be trween Hhe wer tone. (Ram! vel your answa to tuo deaimal plaie.) pa)=1+ X-ズ,…

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Q: 4. a) Prove that i) V=1 ¡¡) fx+nh = Σk=0 I A I+A 1+A (1) Ak fx.

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Q: 1う× ) did Fis erimitive af F af F 2) did p is integrable

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Q: Show the following proposition using a proof by contraiction  Proposition. I a,b, E Z, then a^2-4b-2…

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Q: Coshlutv)= Coshucoshv+ Sinhu Sinhk

A: we will use sinh(u)=eu-e-u2    &amp;   cosh(u)=eu+e-u2

Q: 416 Find PH) 5245

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Q: Let d3+2y (1,)ル

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Q: If f(x) = which one of the following is f-¹(x)? a) b) c) x- x-1 2x x d) 2+3 c) = 2 x+2

A: The given function f(x)=xx-1

Q: XG);t waSin (e

A: The equation of X(t) = t2 – 2t and W(x) is given, now find the derivative of W (X) with respect of X…

Q: 19) fiud eq uilibrium Point for the demond arol Supplie fumetion of Dq = - 1.259+ 475 and S) =…

A: Given D(q) = -1. 25q + 475 S(q) = -1. 125q + 266 For Equilibrium, D(q) = S(q)  0.125q = 209 q = 1672

Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: 1) Find RT Y x+ 19 x + 15 R の

A: Here we have Y is mid point of ST and X is nid point of SR. Then we know that by the property of…

Q: to of 3g dx Be

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Q: Which of the following is a TRUE statement? O A) C-1 = t6 O B) L-1 3 = 3-3e C) 6! = t (s+4)5 s2 + 5s…

A: Here we remind the formula of Laplace transformation of different functions. At the last we found…

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(x) = -x3, (a + h) –…

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Q: Q) let P aprobabiity funckion on S: La,a,a) Find plai) If:- i) pcaz) = and plas) = ii) pc{ãa, az} ,…

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Q: (−1)” - {1- (-²; n = N / is n The supremum of the set S=1- a) 1 b) 0 c) n d) 2

A: We haveWe have to find the supremum of the set S.

Q: let f [o2]→Rbe afunction if x<1 fex)= Is f Riemaninteglable? 下くx か

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Q: b) Compute S i) C = √z: 121=4} 22²+2+1 dz, where iv) c=fz: 121=4} 22+4 ii) C = {z: 17-61-2} \ii) C=…

A: Step 1: Use Cauchy's integral formulaintegral cf f(z)/z-z0 dz = 2.pi.i.f(z0) here f(z) = given…