f lim f(x) = 0 then | f(z) dz converges.

Q: Give an example of a sequence of continuous functions: fn : [0, 1] →R that converges pointwise to 0…

A: Let us consider the function fn(x)=xn on [0,1]. Let u assume that the function fn(x)=xn is pointwise…

Q: Let f(x) = (x − 3)^5 and x0 is not equal to 3. For each n ≥ 0, determine xn+1 from xn by using…

A: To obtain the root of the function fx by Newton-Raphson method, use the following formula.…

Q: 1 dx is convergent True False

A: Definite integration

Q: WNII sin 2 7) Show that 4 VN converges/diverges.

A:

Q: Find the radius of convergence, R, and the interval of convergence, I.  infinity signEn=1 xn/n2

A:

Q: sin (nx + 3) f (x) = is convergent point wise to zero function. %3D n – 1 ylgn O İhi

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Q: dx 2. x +1 -1

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Q: x° e* dx 00

A: Given : ∫-∞0x5exdx

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(æ')…

A:

Q: 0o Inx dx Evaluate it and state whether it converges or diverges. x2 d)

A: That's easy. Have a good day!!!

Q: 1 dx is convergent True 8

A: Solution is given as below:

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…

A:

Q: (x+3) " is: The radius of convergence of n=1

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Q: Prove that sina de converges but not absolutely for 0 < p < 1. XP

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Q: The sequence of functions {f,(x)} where fn(x) = x" converges on the interval [0, 1] to a function…

A:

Q: How to prove that the function h(y)= sum_{m+1} ^infinity (m+y)/(m^2+y^2) converges to a continuous…

A: We are given a series given as, hy=∑m+1αm+ym2+y2 We need to show that the above series is…

Q: dx 4. Determine if the integral converges or diverges. (x – 2)

A: In this question we have determine the integral converges or diverges

Q: sin (nx +3) S,(x) =- is convergent point wise to zero function. %3D п - 1

A: First one is true second is false.

Q: 1 dx et+ e

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Q: If lim,- f(x)=0, then f(x)dx converges Select one: True O False

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: If lim,f(x) = 0, then f(x)dx converges Select one: O True False

A:

Q: A) diverges by divergence test B) converges by CCT C) diverges by ROOT test D) diverges by RATIO…

A: To check the Convergency of the given series, we need to use of integral test. Here is the procedure…

Q: 2x Check whether the improper integral / -dx converges (x²+2)² or not.

A: Given : Improper integral ∫-∞∞2xx2+22dx To find : Check whether given integral converges or not.…

Q: (4)When estimating the root of the function f(x) = (x− 1) ^2 lnx  and using Newton Method, find the…

A: Consider the given function,

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

A:

Q: b) Determine whether the improper integral 1+ sin x 1+ x2 converges or diverges.

A:

Q: of P converges Find the Value which the integral absoluley condition. Sin () dx

A: To find the value of p for which the integral ∫1∞sin(1x)xpdx  converges absolutely. The improper…

Q: By using the substitution x = t² determine the convergence of d.x [ (x + 1)√x

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Q: dX Show that Xe* converges/diverges.

A: Given : an  = 1 / x e(x)^2

Q: arctan(x) dx 2 + ex 20 Jo convergent divergent

A: Answer is convergent.

Q: 1 dx is convergent x" If n>2, the integration

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Q: (x – 3)" Determine the interval of convergence of 2n + 1 n=1

A: Consider a power series . The radius of convergence of this power series is a number R such that the…

Q: Find f xln(x +1)dx

A: ∫x ln(x+1) dx =∫ddxx22 ln(x+1) dx and by IBP: ∫uv'=uv-∫u'v =x22 ln(x+1)-∫x22ddxln(x+1) dx =x22…

Q: 1+x dx converges, you compare the integrand by To determine if 2 (X+2)10 1 (X+2)10

A:

Q: ZK ao L-C K=0 28 (2k)! Radius of convergence

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Q: dx is convergent V2 1 True False 1, 8.

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: Given information: 0≤G(t)≤H(t) for 0≤t≤∞ and ∫0∞G(t)dt converges. Explanation: Suppose…

Q: .2 x+15 dx Jx* +3 1

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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: 1 [3] b) Determine whether dx converges or diverges. Justify your answer 1+x?

A: According to the question, we have to determine whether ∫0∞11+x2 dx converges or diverges. If the…

Q: sin (nx + 3) f (x) V is convergent point wise to zero function. n- 1 صواب ihi

A: True

Q: 11 dx Determine whether is convergent or not. (3 – x)2/3

A: As the value of Integral is finite, it converges.

Q: メー) whatis theradius h.gh of convergense f the power senes) 9.3 b. 2

A: ∑n=1∞(x-1)nn.3nwe have to find radius of convergence of the power 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: Find the radius of convergence for (sin’ n)x". n-1 T

A:

Q: Determine whether the improper integral diverges or converges. e2x dx e-2x converges diverges…

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Q: (b) Explain why the integral e- *x* dx is convergent.

A:

Q: 2x – x3 1. Evaluate dx. (x – 1)² (x² + 1) 2. Use the previous item to determine if the improper…

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Q: -dx converges ex - e- Select one: O True O False

A:

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!