.Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

Q: Q2// Find the Maclaurin series of the function f(x) = x² sinx ?

A: Given: f(x)=x2 sin x Formula used: f(x)=f0+f'01!x+f"02!x2+f'''03!x3+....

Q: | Find the Maclaurin infinite series for the function : y(x) = sinh (n² x)

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Q: (d) Calculate the integral 1 dr, x (In a)P and thus show that it converges for p > 1. Carefully…

A: (d) given integral ∫2∞1xlnxpdx claim- to calculate the integral and show that it converges for…

Q: The series elnz) - e) converge to n=1 (a)Ve - 1 (b) e - et (c)Ve - e3

A:

Q: which of the following SSeries Converge 7n 2n2+1, tan

A: Series and sequences

Q: The sequence V(n + 5)(n + 7) – n} is A) Convergent to 0. B) Divergent. C) limn-»0 V (n + 5)(n + 7) –…

A:

Q: C) Use a known series to express f(x)= sin(x²) X as a Taylor series.

A: Given function is f(x)=sin(πx4)x As, we know  sin x = x-x33!+x55!-x77!+…

Q: 00 Determine whether the improper integral ²+37+1 e dx converges or diverges. Show all your steps.

A: Since there is infinity in the upper bound, this is improper integral of type 1.   To evaluate an…

Q: Obtain the term of the power series of sin(x + 1) where n = 3 for a value of x = 3.20.

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Q: For what values of x does the series ∞∑n=0xn / n+1 converge?

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Q: Which one of the following methods always converges while finding the root of f(x)= 0.

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Q: (-1)"n" sin" (4) 2n n=1 CS Samed with Camacarner

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Q: +o0 (-1)*n" sin" () Σ 2n n=1

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Q: dx converges and, if so, to what. 49. Determine whether J = | E/1* I-

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Q: The series: (-1)" tann n=1 Da. converges absolutely Db. converges conditionally Dc. diverges 8.

A: Answer is following.

Q: The following improper integral (x² – 1)e*+1dx converges to e diverges This option O This option…

A:

Q: 2n2+5 Does the series E- converge or diverge? What happens if I try to use the Ratio Test? Is it…

A: Solve the following

Q: Note that you only have one chance. The power series of sin(x) at x= is given by k=0 (2k+1)! k=0…

A: Given Power series of  Sinx at x=π2

Q: 5. Use the comparison test to determine if each integral converges or diverges b) 2 2/3-4 a) e-x² dx

A: Solution: 5.a ∫1∞e-x2dx

Q: Use the Integral Test to determine whether the seriesconverge or diverge. Be sure to check that the…

A:

Q: Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or…

A: Solve for x = e and check whether it converges or diverges as follows.

Q: 6+ cos (7x) Perform a test to determine if x converges. T/ 7 00 5 dx X II

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Q: Are there any values of x for which E=1(1/nx) converges? Give reasons for your answer.

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Q: The series E-1 and improper integral S dx converges and diverges at the same time.

A: the statement is true

Q: 2 Represent the function as a power series f(x) : (1 – 7æ)2 n=0 e radius of convergence R

A:

Q: +00 4+ cos n 3n - Vn n=1

A: To find the given series be convergent or divergent .

Q: Find the limit of the series Σ[(i+1)/4i] where i goes from 0 to infinity.

A: Note:

Q: Which of the followings are false? 1. E1 sin converges by comparing with II. E1 T%3D1 nl 00 n-1…

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Q: The series ∑Cn(x+9)^n converges at x=−4 and diverges at x=−17.

A: We know that if the power series ∑ n=1∞an (x-b)n is convergent at x=a, then this series is…

Q: d 23 a Show that dx :(-{e-*(sin x + cos x) ) = e¬* sin x. N. 00 b Find e* sin x dx, and show that…

A:

Q: Ehe following DE Solve x" cosy - = 2. dy becing the follo wing Convergent of diveigent Test Series…

A:

Q: B) Find the series' interval of convergence of E (tan-1x)" n%3D1

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Q: If y =1+2x + 4x² + 8x +... i) Show that x= y -1 2y i) Find the interval in which the series is…

A:

Q: 8+ cos (7x) Perform a test to determine if x converges. 3 n/7 9 dx x3 1/7 (Type an exact answer,…

A: Given integral :

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

A:

Q: Represent the function as a power series f(x) = > Cnx" 2+ x n=0 Co = 0 C1 = C2 = C3 = C4 = Find the…

A: We have to find power series reptrsentaion as well as radius of convergence:

Q: The following improper integral dx Vx2-1 diverges to +o converges to V15 This option O This option…

A:

Q: Does ∞ ∑ ((sin^2)(n)/(2^n) n=1 converge or diverge? Use any method and give reasons for your…

A:

Q: 10.Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

A:

Q: n! +5) A) diverges cos 40320 B) converges

A: We will apply Ratio test to check convergency

Q: Write f(x) as a power series and give the interval of convergence f(x)=6/(1+7x^4)

A:

Q: Using the nth term test for divergence, the series a, = 32n+1 n=1 7n=1 is divergent since lim an=

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

Q: ex-e-* Find Maclaurin series for: 1. sinh x = 2

A: Find your answer below

Q: 6. Determine whether each of the following integrals converges. If so, find its value. (a) x In(x)…

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Q: Find the sum of the convergent series. (b) (sin 1)" n=1 9 27 (c) 8+6+;+ Σ (2n + 1)(2n + 3)

A: As per bartleby guidelines we only give first question answers.

Q: 1 - dx converges? What are all values of p for which x2p 8.

A: Given : ∫1∞1x2pdx

Q: ») Does the series S cos(n7) converges or diverges? Vn n=1

A:

Q: (b) Does the series cos(nt) converges or diverges? Vn n=1

A: Test the convergence of alternating series test

Q: Find the first three nonzero terms of the Maclaurinseries for function and the values of x for which…

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.