#1 same holds for all x, y E R. (First prove that a" ay at+y for all x,y E Q, prove that the at+y for all x ER and y E Q.) Let a > 0. Taking for granted that a a

Q: Ⓒ Prove that tan' (2)=1; In Inltiz i-iz

A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

Q: 6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7.…

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Q: Let X=(1,0, – 1, -/2)'. Then, ||X||=v2 Select one: True False

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Q: ) Let f(x) = c) 1 x + 3 following: a) ƒ (-3) = = defined, write "undefined". Evaluate the Undefinec…

A: We have given function  fx=1x+3 (a) Put x=-3 f-3=1-3+3=10 f-3=Undefined (b) fx+h=1x+h+3

Q: 5. Let U ~ U[5, 10] and let X = I5,7) (U) be the indicator function of [5, 7) and let X,…

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Q: Delermine seich all mateuraal neumbers e, y 4 that ayz t scy t Iz tyz tety +złl=2020

A: You must have an idea how to do factor of any equation. The

Q: Intermediate Value Theorem: Let f(r) = r - 2, [a, 6) = [1, 2), and K = 0. (a) Verify all hypotheses…

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Q: prove that 01a| = 0 => a=o @ 1-al-lal @lak b ⇒-b<a<b @la-bla lal-lb/

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Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: 7.2 Give an & - 8 pr at (1 continuous (2x - 2).

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Q: Show that the function f(z) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set f(r) = z and show…

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Q: Let fo) -x1 and go) = 3. g0) %3D %3D @ Derermine if the fanctien f:R>R defined by f) is anto…

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Q: 2.5.33. Prove that the image of the function f: R → R , f (x) x2 is the interval [0 ,1) . Do not use…

A: The given function f:ℝ→ℝ f(x)=x21+x2 We have to show the image of the function is  [0,1)

Q: Q: If f(x)= ax* + withE a, > 0, b >0 +b,x + b, then show that Lt f(x)=o ifn>m. %3D

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Q: #4) What valwes of c Cif anu) are predicted by the Me an Vae Thearem for the function fex) = (x-32)o…

A: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

Q: is harmo Q4) Find the result of the following: Find z for Inz = 1-in? 1. 2. I (7/2) =? (Gamma…

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Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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Q: X Y Z' WXXN W. Y ED O XYZ' + XY + WX'YZ (XYZ)+(X+Y) + WX'YZ F

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Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

A: From the given information, W follows normal distribution with mean µ=-1 and variance σ2=4.

Q: 2(x-1) If y = Vx² – 2x then y' 3x2-2x

A: For the first part, we differentiate the given function y with respect to 'x' and use change rule of…

Q: Q1. By computing appropriate Lipschitz constants, show that the following functions Saisty Lipschitz…

A: Solving the first question. Part C is not clearly visible clear. Please follow the methods in parts…

Q: Q4. Prove that f(z) = Iz/2 never be holomorphic function at z = 0. %3D

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Q: Je fine a binary relation Rond by R= [(y)] ER² x ус

A: Given is : R={(x,y)}∈R2:x-y∈Q We have to show that it is an equivalence relation.

Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

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Q: Prove that for any x > 0, y>0 (x² + y²) ³ ≥ (x³ + y²³) ³. Hint: Introduce a new variable z = (2)².

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Q: Please prove it (c) x = y z and |x| = y + z imply y = x+ and z = x¯. −

A: What is Real Number System: A real number is a value of a continuous quantity that can be used to…

Q: Q/ If the joint p.d.fof X and Y as f(x,y) = }*y (cx?y ,x2sys1 ,0. W find the value of c and P(x 2…

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Q: 8. Find a function g such that og = 2² - sinz. Əz 9. Find a function h such that Əh əz 10. Find a…

A: 8. Given that ∂g∂z=zz2-sin z. We have to find a function g that satisfies the given condition. Note:…

Q: How many antiderivatives does a function of the form f(x) = x" have when n 0? A 1 B may vary…

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Q: Hw4 Prove if x;-→x then if xj ->x Hw4| Prove and HoS Prove if x; →× y;→y > X

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Q: Z is the set of integers, R is the set of real mumbers. 1. Functions f, 9, and h are defined as f:R…

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Q: Let o e C (RN), he RN - (0}. For teR', we set (r+th)- (x) (x) 1- Show that e C (RN).

A: Since, you have post multiple question. I am answering first one. Please post again for the…

Q: Suppose that it + [[ f(x, y)dA - 26 and ₂⁹(2, 3)dA R R (A) The value of [kf(x, y) + g(x, y)]dA is […

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Q: Show that and deduce that V-U <tan¹v-tan¹ u<-- 1+v² π -+ 4 3 25 < tan -1 3 V-U 1+u π <-+- 4 6 " " if…

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Q: Exercise 4.1.5. Which of the following formulas define functions R → R? (2) p(x) = (x^(2)+3) / (x+5)…

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Q: 1 X+8 and h(«) = x- = 12) If what is the value of g(h(- 8))? 1) 0 2) 9 3) 5 4) 4

A: Simply first find the h(-8)  to put x=-8  in h(x) then put it   in g. And calculate to get the final…