17. Find all critical numbers of x) =x– 2/x. A) x= 0, 1 B) x=0 C) x= 1 D) x=2 E) No critical number 18. A number c that satisfies the conclusion of the Mean Value Theorem for the function Ax)=x² + 3x – 2, 0

Q: 4. Show that z = a' Zax if z = e-al cos(x-at) %3D

A:

Q: 2. Show that by using MEAN VALUE THEOREM . u-v < tan-1 v - tanu < if 1+v2 u-v 1+p2 0< u<v and ded…

A:

Q: A population consists of 4 units with values 156, 149, 164 and 155 respectively. Draw all possible…

A: Given that Population size N = 4 Sample size n = 2 Then possible samples WOR are NCn = 4C2 = 6

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A:

Q: what happened to the 1(1-lambda) part in the first line

A: Given

Q: 15: Using first principles (by definition), prove thát thể đêrivätive of ä constant is U

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Q: find all the Second order partial denvatives of the givén funcion fua、り) %3D

A: The given function is f(x,y)=exy

Q: 4. (a) Use Gauss's lemma to evaluate (), showing all working.

A: The given term is, 1119

Q: Prove using the IVT,  √2 exists.

A: To prove using IVT, 2 exists.

Q: The product of sum (max term) form of the boolean function F = x +y'z is

A:

Q: in in Signed-Rank Test a two-sided alternative, we may reject H0 in favor of H1 if either w+ or w-,…

A: Signed rank test for  two tailedHo:M≠Mowe reject Ho, if W+≤Wα and W-≤Wα

Q: Let {Xi} be i.i.d.∼ Exp(θ) and ai > 0. Denote by Z = min{a1X1, . . . , anXn}. Suppose that sum 1/ai…

A:

Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: 2. Find the desivative ofy= Binx

A:

Q: 94) Show that F= ;². ?' is Consenvatwe and gind potintial - the sealar

A:

Q: Use Simpsons 1/3 rule to evaluate of e-x2 over the interval 0.2 to 1.5 using 6 segments ?

A:

Q: In R, the model mod <- Im(z ~ x + y) will contain: O the results from regressing the dependent…

A: Introduction: It is required to identify the correct option.

Q: Prove %3D 11

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Q: find rank(AT) and nullity(A)

A: Rank of A = rank of A^T use this relation

Q: (W/) Express In x in terms of In x, In y, and In z. - In y + 1. In z 2 2 In x + 1 2 In x- In y + In…

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Q: .4. consider the funchon f(x)= Vox-18. for the domain [3,00). Find (x), Where f.-! is the Įnverse of…

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Q: B) Show that coth-x = In ()

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Q: graph the inequality on a coodinate plane x &gt; with line under it 2

A: To graph the given inequality x≥2.The equation x=2 has a graph that is a vertical line with all…

Q: Hew.b prove that CAXB)-Ais atways-Zero

A: Topic:- vector  algebra

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: 6. Prove: 4 |x – y| 0, then x = y Vx, yER

A: To solve Q.6 Prove: If x-y&lt;ε, ∀ε&gt;0, then x=y ∀x,y∈ℝ If (Given) Then (To prove) ∀ε&gt;0,…

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

A:

Q: b)use Cauchy Schwarz inequality to show that if Let u = and v = inequality to show that a² + b?

A:

Q: Let f be q functiom that admits contırous second partial denvatives Df (X.Y)=(4x²- 2q²x+ 2q°y ,4y³ +…

A: Given, the second partial derivatives              ∇f(x, y)=4x3-2a2x+2a2y,  4y3+2a2x-2a2ywith a&gt;0

Q: Prove that interval [0,1] is uncountable.

A:

Q: (b) State Heine-Borel Theorem.

A: (Heine-Borel Theorem). A subset A of R is compact if and only if A is bounded and closed (with…

Q: Let X be the amount of soda released by a soft-drink dispending machine into a 6-ounce cup. Assume…

A: Given information: σ=0.25 a)  P-value for the quantity, where no more than 0.5% of the releases…

Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: 1. Iff: [0, 1] R is defined as f(x) = x if x is rational, 1-x if x is irrational, discuss the…

A: Given :  f: [0, 1] →ℝ  is defined as     f(x) = x,if x is rational1-x,if x is irrational To find :…

Q: 12) Show that D- ldi-dal between is shortest distance a x+ by + e2 of i ancd ax +by +Cz = dz?

A:

Q: (a, 0) is not measurable.

A: In this question, we check the given set is measurable or not. here we use the condition of Lebesgue…

Q: 17. Use Theorem 4.7 to prove that Vx + 3 2 V3 + x/4 for

A: Let,

Q: A (σ,ρ) regulated source is served at a network link with transmission rate C >ρ. Show, using…

A: Given: Here the given is at a network link with transmission rate C &gt;, a (,) regulated source is…

Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

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Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximuma possible…

A:

Q: 6. Use the IVT to prove that x2+ In r = has a solution. %3D

A: The Intermediate value theorem says: If the continuous function attains two values then it must…

Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: 17. Prove thatsin x = =x 1-x2 dx

A:

Q: 4. Prove: -| s|x - y| Vx, yER

A: Solve the question number 4 as asked by the user

Q: (1) Write the Cauchy theorem (without proof).

A: Dear students you have asked multiple question, as per our policy your first question will be…

Q: A prove that Newboń's for ward formal?

A: Note: Since you are asking the prove for Newton's forward interpolation, but the given formula is…

Q: 3)suppose fle) isadifferentialle fmehon on the intervall E-7,J Such that Hl-7) =4 and fl)=1.…

A: Intermediate value theorem

Q: -. Show that both R and R2 may be covered by countably many open balls.

A: Soution.