Find P(2 < X < 5) using the cumulative function given by

Q: Find the power series representation for the given function: 1 f(x) : %3D (1+x²)2

A: We know:∑k=0∞ark=1+ar+ar2+...            =a1-r Derivative of a power series is term by term…

Q: Represent the function 5x 00 as a power series f(x) = >, 6+ x Cnx" n=0 1 = 2 = 3 = 4=

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Q: Use the ratio test to determine whether an converges, where an is given in the following problems.…

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Q: What are all of the values of x ,such that E-1)n+1(n)* converges? x1.2 O x<1.30 x<0,40

A: By lebnitz test we observe n^x tends to inf gives zero only when x&lt;0.

Q: Find 2x dx. x2-4 (if it converges)

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Q: (1 – x + x²)y" – (1 – 4x)y' + 2y = 0.

A: Given differential equation is (1-x+x2)y''-(1-4x)y'+2y=0               (1)y(1)=2, y'(1)=8 Let the…

Q: #2

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Q: The series 2 ÷, n =0 x" |x| >1 has a sum equal to: Select one: а. х b. х— 1 C. 1 1-x d. 1 х —1

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Q: Find the values of x for which the series converges. E(-3)"x" n = 1

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Q: Find the power series representation of the function. f(z) = 1+x2

A: The objective is to find the power series of the function f(x)

Q: Find a power series representation for the function f(x) %D 1- x3

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Q: Apply the power series method. Show the details. y" + y = 0

A: The given differential equation, y''+y=0

Q: Define effective interest rates and prove that r = i -1. 1+ n

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Q: Let f(x) be the function which is represented by the power series : f(x)= E (-1)"(x-2)" Zn=1

A: Given f(x) function represented by the power series We need to find the 5th derivative of f(x) at…

Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

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Q: Let S f(x) dæ = S". f(x) dx + So® f(x) dx. If S". f(x) dæ is convergent, then Select one:

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Q: (c) Show that fn (x) : x2+n? converges uniformly on [0, 0).

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Q: For each n ≥ 1, let fn : R → R, fn(x) =nx/(n + x^2) Show that the sequence of functions {fn}n≥1…

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Q: H.W Given a sequence x(n) for 0sns3, where x(0) = 1, x(1) = 1, x(2) = -1, and x(3) 0, compute its…

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Q: 32. Find the limit of the series: x (1+x) (+x) 1+x2 A) B) xx X+x C) (1+x D) (1+x) E) x

A: Given series is,

Q: If f(x) ≤ g(x) for all x in [a, +∞o) and converges. •+∞ f(x) da converges, then [*** g(x) dx also

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Q: Find the odd and even half range expansion, f(t) Lt KIN RIN

A: Given:   To find: The odd and even half range expansion

Q: Show that if $a_{n}&gt;0$ and $\Sigma a_{n}$ is convergent, then $\Sigma \ln \left(1+a_{n}\right)$…

A: Here, we are given that an &gt; 0 and series is convergent. We need to prove that: is convergent.…

Q: 1 Determine by the direct comparison test if Ln=1 2n+1 converges or diverges .

A: The given series is ∑n=1∞12n+1 We have to test the convergence

Q: If {fn}n=1 is a pointwise convergent, then {fn}=1 is uniformly convergent.

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Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: Solve the ODE using power series y'=y+1

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Q: E (n!)² (K)! Fan what e is convergent ?

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Q: Given the cumulative distribution function (c.d.f) if x x. 0, x+4 F(x) = 6 1, Compute P(X = 1).…

A: The value P(X=1) is::

Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: (2+x) y" + (2 + x) y' + y = 0, y(-1) = –2, y' (–1) = 3

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Q: +00 3 E(-1)"+1, n n=1

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Q: Suppose that an initial deposit of $100 is made, and a deposit of X is made at t = 2. Find X if…

A: Given that : Principal value = $100  when t = 2. Amount = $350  when t = 4 To find X = ? To use the…

Q: B) > n! (4x – 6)" is convergent for x = n=1

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Q: Find the values of x for which the series E(-1)". (п + 2)(ӕ — 3)" п(п + 1)5" converges. n=1

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Q: There is no value of r such that Jo (3t)-r 5 dt converges. 14.

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Q: 2. For p>1, is S dx convergent? Inx xP

A: To show that whether the given integral is convergent for p&gt;1.

Q: fn (x) = e-na", E = [1, 0)

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Q: The Fixed Point Iteration method always converges when f(x)-D0 is transformed to x=F(x). True O…

A: The fixed point iteration theorem is very significant in solving an equation numerically. Here, we…

Q: If E, 2"an converges and Eo(-1)"2"an diverges, then the radius of conver- gence of Eo anx" is 2. =0

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Q: If E, 2"an converges and E o(-1)"2"an diverges, then the radius of conver- gence of o anx" is 2.

A: According to the given information, Suppose,

Q: Applying the limit comparison test, show that the series 1.1 1 2n diverges.

A: The given series is: 12+14+16+...+12n+... The series ca be written as: ∑n=1∞12n

Q: Find the values of p such that E(-1)"- converges.

A: The given series :

Q: Determine the values of p for which f(x)da converges where f(x) = = 1-e-z TP

A: Here, in the question for what value of p the integral is convergent. The simple improper integral…

Q: Use the ratio test to determine whether converges, where an is given in the following problems.…

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Q: The series solution of DE: x´y" – y=x – 1 is defined by

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Q: 9 Find the power series representation of the function f(x)= 3+x2

A: follow next step

Q: f(x)= x²/1+x³, power series representation is?

A:

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.