Show that Lindeberg's condition follows from Lyapounov's condition.

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Define the term standard linear approximation?

A: we have to define the term standard linear approximation.

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: Stoke's theorem

A: We have to verify the Stoke's theorem for the given vector field. It is given that

Q: Show that f:Z-->Z ; f(x)=x+2 is invertible

A:

Q: (- 0,a) is measurable.

A: Note that, every interval is measurable.

Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: Is it possible for φ(n) (the Euler's totient function) to be bigger than n?

A: The objective is to find the possibility (if any) for φ(n) (the Euler's totient function) to be…

Q: Find mean and second moment of X.

A:

Q: What do you mean by euler's theorem?

A: Euler’s Theorem is a generalization of Fermat’s little theorem dealing with powers of integers…

Q: The moment generating function is always exist

A: The moment-generating function of a real-valued distribution does not always exist.

Q: Define Testing for cointegration when θ is unknown ?

A:

Q: What does the Extreme Value Theorem say?

A: Give the statement of Extreme value theorem.

Q: State Fubini’s theorem.

A: Statement of Fubini's theorem

Q: In your own words, describe Rolle’s Theorem.

A: To describe: Roll's theorem

Q: How is the Chain Rule applied when finding dydx implicitly?

A: According to the question, we have to explain the chain rule when used in the implict function.…

Q: When using Simpson's rule we must having two distinct po.

A: Simpson Rule  Simpson Rule gives the area under the curve. One of the formulas used to find the…

Q: Explain why the fundin f(2)= 526+ z COSZ - z’e? is entire ?

A:

Q: B)Is w = Zez analytical function or not?

A:

Q: Explain why the two forms of Green’s Theorem are analogs of theFundamental Theorem of Calculus.

A:

Q: 28 dt dz -1

A:

Q: Define Wronskian of Linearly Dependent Functions?

A: We have to define the Wronskian of linearly dependent functions: Let f1 ,f2 ,...,fn be n real or…

Q: Explain Fubini’s Theorem.

A: Fubini's Theorem: If f(x, y) is a continuous function on a rectangle R=[a, b]x[c, d] then the double…

Q: prove that for any fixed x > 0. Fix a constant r>1. Using the Mean Value Theorem era > 1+rx

A:

Q: Apply Gauss's theorem to evaluate. A

A:

Q: State the two conditions required for performing a paired t-procedure. How important are those…

A: From the question,Paired t-procedure is the dependent sample t-test, is used to estimate whether the…

Q: The value that will satisfy potential function p is

A:

Q: Use the Max/Min Inequality to approximate the value of fi tan x dx

A: Please refer the attached image for complete solution.

Q: line diagnosed as being due to an initial repair that was incomplete. What was the probahility that…

A: HERE USE PROBABILITY TREE define events as follows I = incomplete repair H = initial  repair service…

Q: Briefly discuss the origin/history of De Moivre's Theorem.

A:

Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

Q: Which of the following is an example of a continuous variable?

A: Here use basic of continuous variable and discrete variables

Q: What does it mean to eliminate the parameter? What useful information can be obtained by doing this?

A: Query- What does it mean to eliminate the parameter? What useful information can be obtained by…

Q: Show that div (r x a) = 0

A:

Q: A random sample of 1000 households was taken and the dollar amount spent monthly on intemet service…

A: Given: Sample size = 1000 households Dollar spent monthly on internet service was recorded for each…

Q: Derive the standard five point formula for Poisson equation with one-dimensional spacing h and k in…

A:

Q: What is the value (i.e. what do we learn) from using the Wronskian on a set of functions?

A: Let F = { f1, f2, f3, ...fn} be the set of functions. 1. If W(f1, f2, f3,...fn) =0 Then we say…

Q: (- 0 ,a) is measurable .

A: Given a statement

Q: Use Simpson's rule to calculate

A: Given,            ∫02x2sinxdx

Q: Suppose that mZT does not equal mU.

A:

Q: What are the Continuity Conditions?

A: When a graph has no holes, no asymptotes or the graphs that does not have breaks are called…

Q: What are Continuous Variables?

A: Continuous variables are numeric variables that have an infinite number of values between any two…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.