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A: f(x)=4x3+6x2-6x-4f'(x)=12x2+12x-6f'(x)=012x2+12x-6=02x2+2x-1=0 x=-2±4-4(2)(-1)2x=-1±32     (critical…

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…

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Q: O s/Vn 12

A: The standard error is denoted by SE

Q: D prove tHhat kin

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

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: Show tH In k CHint dbtain o formdar for Sn Hint dotau forunlar

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Q: The value(s) of x that satisfy In(x² + 1) – 2 In(x) = In(16) – In(8) are/is

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Q: Prove the following version of Darboux's Th

A: To prove the Darboux's theorem:

Q: If A= then A" + nl is equal to

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Q: 2. Use Cauchy- show that each of these funedioca is. nowhere analati -Rlemman.cqmtione to bfi27=2xyi

A: Nowhere Analytic functions

Q: Suppose you tossed a fairdie G00 times and the results are as follows:1= 95, 2=72,3=103,4=105,5=97,…

A: Chi square goodness of fit test

Q: (a,b) is measurable.

A: (a,b) is an open interval.  Open intervals are measurable.

Q: Let X1, X2, be a nequence of ... independent and identically distubuted rvs, each having frñite mean…

A: The Chebyshev's Inequality:                    Let X be a random variable. If X has finite mean μ,…

Q: When using Simpson's rule we must having two distinct point Select one: True False

A: The formula for Simpsons 1/3rd rule is ∫ydx = h3f(x0) + f(xn) + 2(f(x2) + f(x4)+..f(xn-2)) +…

Q: Show that :(i) Fishers IN. lies between Laspeyre's and Pagsche's Inder numbers.

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Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: If Z = eax + by F(ax - by); the value of %3D az is + a ду az

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Q: (b) Evaluate de using Simpson's one third rule with 6 intervals.

A: Given-             ∫031x3+4dx. Evaluate Using Simpson's one third rule with 6 intervals.

Q: sent that by a positiv ntity N(0) is 2.

A: Given as, dNdt=?N0=?

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A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: Which condition would prove AJKL ~ AXYZ?

A: Here we have to find the ratio between two sides such that the given 2 triangles will become…

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A: Simpson's rule is used to calculate the value of definite integral by approximating area of the cure…

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: If delta is large according to Cohen's classificantion, then the difference between u1 and u0 is…

A: Given that - If delta is large according to Cohen's classificantion, then the difference between u1…

Q: (a, b) is measurable.

A: The answer is given as follows :

Q: let X be 4-VV flon)= To Finel ECX) oedECXY)

A: f(x) = x/10 where xx = 1,2,3,4

Q: If ADEF ARST, then we can conclude that ZR

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Q: - Prove thas the scries 2+x2 3+X2 4+x niformcy conuergen2 in any interval?

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Q: Let 9,n be antegers wth 2n and ged (a,n)=1. Show tht of U(Z.) ={a*+nZ:tez} then o#1 mod 6) for all…

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Q: For for any pestive integor n Show that %3DFHE nth fibonacci term fn=the

A: We need to show that , for any positive integer n ,  f1 f2 + f2 f3 + ....... + f2n-1 f2n = f2n2…

Q: Find the deriratire of y tanx usim the Difinition Rule

A: Given that:y=tanxTo find its derivative.

Q: Fincd dy for y-sinner} er tot

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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…

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Q: 24. Find the Fowrier r fas - -IN X

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Q: (a) Verify that Ex = 477, Ey = 86.8, Ex² = 62,029, Ey² = 2028.68, Exy = 11036.6, and r = 0.93853. Ex…

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Q: 5. Demonstrate that Im(iz) = Re(z).

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Q: 7 Gi ven that / f(z)dz =, what is / f(r)dr? 3'

A: Given∫48f(x)dx=73

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A: We have two order relations, one on set A and other on set B and we have a function f from A to B.…

Q: 2. Find the exact \ength af the following curvis

A: Arc length L=∫ab1+dxdy2dy

Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: -64- Eke n Calcul afe th udlue of Z.Z ?

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Q: Since, F is bounded both in LOR) and in lIR), it is Latnded in LLIR) forall fe[1,0) (Prdtem 31).

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Q: Use Simpson's Rule with n = 4 to evaluate [² (t³ + t) dt

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Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.