the Po lowing for being Test series Convergenl- divergent or (4n-5)" (오nti)^ Cos W W:

Q: Using that tanx=x+x^3/3+(2/15)x^5+. . ., find the first four terms of Maclaurin series for sec^2x.

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Q: 16) E(-1)"-1

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Q: Use INTEGRAL TEST to determine whether the given series converges or diverges.

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Q: Show that the series sin2x+sin4x+sin6x+... converges to tan2x if x≠(π/2)+nπ

A: Here I am attaching image so that you understand each and every step.

Q: (7) Express the function h(x) = -1 tan(2x) as a power series. Show your work. Hint: tan(2x) = |…

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Q: Use the Root Test to determine whether the series convergent or divergent. n²+5} 6n² + n-1 Identify.…

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Q: Help please

A: To determine whether the given series is converges or diverges.Consider the function

Q: The series from n=1 to infinity of [(-1)^n(8n-1)/(3n+1)] is given.  Use it to determine the…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 4nt 2) Identify lal.…

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Q: Determine whether the series is convergent or diver gent by applying either the comparison test or…

A: WE WILL USE LIMIT COMPARISION TEST  If we have two series ∑an  and ∑an with  an≥0 and bn>0 for…

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series.

A: Given: We have to use Limit comparison test. To find: convergence or divergence of the series.

Q: Use the Integral Test to determine the convergence or divergence of the series Σ k=1

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Q: +oo Σ 8n2 16n + 6

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. sin (n) n =…

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Q: 15) En=1 2n2 00 3n2-1

A: Given : Limit equation is given Where ,an = 2n2 / (3n2 -1)

Q: Use test of coarse divergence to show divergenceof the series.

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Q: F6)= 1-2x

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Q: Determine whether the series (sin 3n)" \ nn n=1 is convergent or divergent.

A: The question is about whether the given series is finite or infinite in which we have to find the…

Q: Tind the vudivs and interval of convergense of the powe Series, (-2)" (x+2)" San

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Q: 6. Σ(-1)n-1 sin (2) n=1

A: Explanation of the answer is as follows

Q: the Pollowing for being Test series Convergenl- divergent or (4n-5)" (2n+1)" nニ 1- Cos

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 00 11 (n + 1)82n + 1…

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. > sin n = 1…

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Q: E sin n=1

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Q: 08. Σ 3n 1 Arcsin 2n n=1

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Q: tan-in The series is divergent by ratio test 2

A: For any series ∑an, the ratio test is done by evaluating L=limn→∞an+1an. If L<1, then the series…

Q: Use power series to evaluate lim X- 0 cos x - 1

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-7)" n2 n = 1…

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Q: Write the first two nonzero terms of the Maclaurin series for f(x) = arcsin x. Justify your work.

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Q: Given that 2" with convergence in (-1, 1), find the power series for with center 1- 379 0. 00…

A: Given that 11−x=∑n=0∞xn with convergence in −1,1 We have to find the power series of the function…

Q: Use the Root Test to determine if the following series converges absolutely or diverges. (Hìnt: lim…

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Q: Find an example of a function which is Continuous at x=0, infinicely clifferen tíable lat X=0 but…

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Q: State the Taylor series tor flx)=cos x at x=0. (Yu don't have to derive it.) =COS Using this, find…

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Q: Represent the function 8ln(8−x) as a power series (Maclaurin series) What is the radius of…

A: Given:- The function is, f(x)=8ln(8-x) as a power series. To find: - The radius of convergence of…

Q: 9. For the convergent series ETo- find an upper bound for the error |S – S3]. Show work. 00 n4

A: According to the Alternating Series Estimation Theorem: If the Alternating series ∑n=1∞(-1)nan…

Q: Find the Taylor series along with its radius of convergence and interval of convergence 1 centered…

A: Given: f(x)=14+x centered at x=3 Formula used:…

Q: Compute the 10th derivative for f(x)=arctan(x^2/7). Hint: Use MacLaurin Series for f(x).

A: we know that, arctan(x) has a series as below,    tan-1(x)  =  x-x33+x55-x77  .... hence,…

Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-9)" n2 n- 1…

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Q: The harmonic series is: O Convergent by the Integral Test O Convergent since the corresponding…

A: To choose the correct option

Q: Determine whether the series is convergent or diver gent by applying either the comparison test or…

A: 2.) Given series is ∑n = 1∞1nn As n > 2    for all n≥3nn > 2n   ⇒ 1nn < 12n ⇒  ∑n = 1∞ 1nn…

Q: Find the Maclaurin Series for "indefinite integral xarctan (4x2)dx

A: Maclaurin series of function fx is a Taylor series of function fx at:…

Q: solve the problem by use the hint

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Q: Find the Maclaurin series of sin²(x) and it's interval of convergence. [Hint: a

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. 00 1 Σ sin n…

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Q: When the integral produce a finite result, the series is convergent FO

A: We are entitled to solve only one question at a time so, I am providing you an answer of the same.…

Q: 8. 3n2 -n 6n2 + 7 n=1

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Q: solve the problem by use the hint

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Q: Use the Root Test to determine whether the series convergent or divergent. Зп -4n n+1 n 2 Identify…

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Q: Let be a power series with the radius convergence R= Then the series n=0 converges at

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.