2.5 Critique the following "proof": x² > y? 2² - y? > 0 (x+y)(x – y) > 0 x+y > 0 x > -y

Q: (c) Prove the inequality I +y +x > Vryz 3 if x > 0, y >0 and z > 0.

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Q: True or False. Show your proof. X[n,0) → 0 in L'(R)

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Q: Q4/ if f(x.y)=x-y and g(x.y)=3y prove V2) gVf-fVg g? %3D

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Q: Evaluate h(2), where h = (gon. s (2) = –ig(2) =?+1 1 f (z) . h(2)

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Q: 2) vting daplace toansfóöre, Solve x" Zt)+4x'Lt)+3=(4) uing = 10 gint yeren that xco) = -3t Ans: ILt…

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Q: using the false - position to doter mine the voot of the eqution fcx) = 0-7 x5- 8X* +44 x-90 x+82 X…

A: Suppose the root of the function f(x) lies in the interval xl,xu. To obtain the solution of the…

Q: Q.3 а. Using first principle develop a formula of finding AY AX when Y- {(X)+g(X) Z(X)

A: y = (f(x) + g(x)) ÷ z(x)     Hence,  => ΔYΔx  =  dydx  =  ddx(fx+gxzx) By quotient rule of…

Q: Determine the particular solution1 1. (2-r) dr=rsin 0 de; when 0 0 and r 1

A: The given differential equation is 2-r2dr=r2sinθdθ. Rewrite the above differential equation as…

Q: 15 Using intermediate value theorem, the equation x² + = 4x has a solution over O 1,21 O 10,1[ 13,4[…

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Q: 5. Evaluate the integral. x+7 (x-6)(r-2)*a

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Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: 15. f(x, y) = xy /x² + y V9 – x² – y? 16. f(x, y) ▪ x + 2y + y? x² – y? 17. f(x, y) *

A: 1.  fx,y=xyx2+y2.  fx,y=9-x2-y2x+2y3.  fx,y=x2+y2x2-y2

Q: eiw Фx (») %3D 1+ 4w? 11) Prove that the mean of X= 1.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6.10. Prove that (a) J,"(x) = ¿[J,2(x) – 2J,(x) + J, +gl«]. %3D n-2

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Q: 2 21. The maximum value of- is 3 cosh 2r + 2 A 2 в 5 D

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Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: 1. If x is an exact measurement of a certain quantity and x0 is its approximation, the concept of…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

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Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

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Q: f(2) — и(х, у) + jo(x, y) и(х, у) — е% сos x — х f (0) = 1

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Q: Q-2: For what values of a, m and b does the function: 3, f(x) = -x² + 3x + a, 0<x <1. (mx + b, 1<x<…

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Q: Q.3 а. Using first principle develop a formula of finding AY AX when Y-LX)+g(X) Z(X) f(X)+g(X)

A: Note :- Due to having multiple sub parts i am providing here solution of part a only

Q: Find solution n f(x) 300 2.4771 x (301) using newton backward 304 2.4829 305 2.4843 interpolation…

A: Introduction: Interpolating polynomial is the polynomial having the least possible degree that…

Q: əz ax+by+sin(ax +by) show that b əx Q5-A) If z = (ax +by)² +e+by+sin( ax a Əz dy

A: The given problem is to show the following condition for the given multivariate function of z.

Q: h2 |w(x) = Let h = x1 – xo, and w(x) = (x – x1)(x – xo). Proof that max %D 4

A: Let w(x)=x-x1x-x0 where h=x1-x0Prove that wx=h24.

Q: 1. true or false. justify your answer. (a) |x+iy| ≤ |x| + |y| (b) arg(-2+10i) = π – tan−¹(5) + 2nπ…

A: Given statements,  (a) |x+iy|≤|x|+|y|  (b) arg(-2+10i)=π-tan-1(5)+2nπ for n an integer. The…

Q: 1. Use calculus to identify the absolute extreme values of ƒ (x, y) = y³ — 3xy + x³ on the triangle…

A: Given function is fx,y=y3−3xy+x3. We have to identify the absolute value of fx,y on the triangle…

Q: A useful consequence of Taylor's theorem is that: |æ – c|" max|f(n+1)(2)| (n + 1)! > (æ)"y| (1)…

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Q: 5) s how that the line of intersection f the Plas and 5x-2y-Z=0 is Parrliel to theline X+2y-22= 5…

A: Given that plane  ,P1:x+2y-2z=5plane , p2:5x-2y-z=0line ,l:x+32=y3=z-14Normal of P1  ,…

Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: 2 21. The maximum value of is 3 cosh 2r + 2 A 2 B 5

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Let x, y range over N and define Q(y): 3x. x < Y. Choose all the values for y such that Q(y) is…

A: We know that set of natural number is {1,2, 3,4,5,6,7,.......}

Q: 2. (8.7.10) Let f (x, y) In y R is the rectangle defined by R {(x, y)|1 < x < e2 and 1 < y < e}.…

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Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

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Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: 13.4. Let f(z) = y – x- 3ix? and y be given by the line segment z = 0 to z = 1+ i. Evaluate |…

A: Let us consider the given function f(z)=u+iv then the integartion of the function over the curve C…

Q: We hae a theorem that offers conditions when the IVP: x'- f(t, x), x(to) = X , has a unique…

A: See the attachment

Q: I. Find the absolute max and min for f(x,y) = xy² on D ={(x,y): x >0,y > 0, x² + y? < 3}. Justify…

A: Given- f(x,y)=xy2  to find - Absolute maxima and minima for the given function if onD={(x,y):…

Q: 1+ In x If y = 1- In x The value of y' = 10.62 at x = 2 %3D

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Q: ди n. = 3 Ôx? para t> 0, 0<x < 3 ди ди (0,1) = (3,t) = 0 u(x,0) = 3x +1

A: Solution

Q: 7. Compute , and- axay : f(x,y) = (x + y)(2x + y)² ax 'ay

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Q: 7. Use appropriate formula of geometry to evaluate the followings. L(lx – 3| + V36 – x²)dx b. L(2x +…

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Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: 3) Find the deri vative of cscC (x) (xf3)' X4

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Q: Q1. Consider the two different losses: (i) zero/one loss where Ai dij = 1 and (ii) generic loss…

A: Given Consider the two different losses: (i) zero/one loss where A₁ = 0 and Aj = 1 and (ii) generic…

Q: 17. f (1,y, z) = x subject to z? + y? + 2² – z = 1 %3D

A: Let h(x, y, z)=x2+y2+z2-z. We now have ∇f(x, y, z)=(1, 0, 0) and ∇h(x, y, z)=(2x, 2y, 2z-1). Let λ…

Q: 1. a)For what interval(s) is h(x) = 2x + 10 positive? b) For what interval(s) is h(x) = 2x + 10…

A: Given 1. h(x)=2x+10 and 2. y=-x2+36

Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!