Q: Does / dx converge or diverge? Justify. -7 0, x' + x'
A: Plot the graph of the function.
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Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?
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Q: 4 dx
A: Use limit comparison test and p series test
Q: Use series to evaluate the limits
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Q: 9. Evaluate the following integral and state whether it converges or diverges. xe dx Check your work…
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Q: Determine whether or not the infinite series below converges.
A: Divergent test: If
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Q: cos NII N 2) Show that converges/diverges.
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Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…
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Q: PART III: Decide whether each of the following converges absolutely or con- ditionally. Justify your…
A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…
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A: Given: Improper integral ∫-∞01000exdx
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Q: 59. Show that 1- sin x dx converges. x? 00
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Q: .Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.
A: Here for the series we use Dirichlet’s Test:
Q: Determine whether sin r dr. is convergent.
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Q: IV. Determine if the given is convergent or divergent. sin(2 tan-1n – TI) Σ (2 tan-1n – Tt) #3. n=1
A: Given : The given series is ; ∑n=1∞un = ∑n=1∞sin2tan-1n - π2tan-1n - π To find : To check whether…
Q: Use the root test to determine whether . converges, where an is as follows. (1 + Ink)*
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Q: [6.6] Determine whether the following integral is convergent or divergent. If it is convergent,…
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Q: 6 Jlgul sin (nx +3) 1,(x) =- is convergent point wise to zero function. n-1 ylgn O Ihi O
A: Calculate limn→∞fn: limn→∞fn=limn→∞sinnx+3n-1 =0
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: IV. Determine if the given is convergent or divergent. sin(2 tan¬1 n – 1) #3. )) (2 tan-1 n – T) n=1
A: Given series is ∑n=1∞sin(2tan-1n-π)(2tan-1n-π)
Q: Use the Comparison Theorem to de x + 1 36 dx Ji O convergent O divergent 8
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Q: IV. Determine if the given is convergent or divergent. #3. S sin(2 tan¬1 n – n) Σ (2 tan-1n – 1) n=1
A: Solution is given below:
Q: Find the exact value that the sequence sin" 1 converges to. (Note that as usual, sin" x means (sin…
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Q: Investigate whether the following integral converges sin I
A: We have to investigate whether the given integral ∫0∞sin2xxdx converges or diverges.
Q: Example :- In each of the frollowing, find the radius af Convergence e and interval of somuengent.…
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Q: dx To determine if converges or diverges, it would be useful to compare the integrand directly to 1
A: Given integral ∫2∞dxx2-1 We have to find it's converges or not . We just use comparison test to…
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A: cosx=1-x22!+x33!-x44!+--- ∑n=1∞1np converge if p≥2 Given ∑n=1∞cosn2n2+4n
Q: 3) Use the Comparison Test for Improper Integrals to determine whether the following integral…
A: This is a problem of improper integral. We will assume another function g(x) and try to prove that…
Q: (8) Find all k so that aek= dx converges. In this case, find the value.
A: Given problem:-
Q: Check whether the improper integral 2x dx converges or not. (12+1)
A: Thanks for the question :)And your upvote will be really appreciable ;) It converges
Q: a. Evaluate the integral and state if it converges or diverges ∞∫0 ex / (1+e2x)
A: ∫0∞ex1+e2xdx=let u=ex du=exdxif x=0 then u=e0=1if x=∞ then u=∞…
Q: use the Comparison Test to determine whether or not the integral converges.
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Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…
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Q: Find the exact value that the sequence sin" 1 converges to. (Note n=0 that as usual, sin" x means…
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Q: 1 ) *It can be shown that the improper integral e sin xdx =. Can we conclude that 2 Le" sin n…
A: Integral test
Q: Which test to use and is it convergent/divergent? Σ 16n2 – 8n – 3 n=1 - -
A: Use the ratio test, L=limn→∞an+1an=limn→∞116n+12-8n+1-3116n2-8n-3=limn→∞16n2-8n-316n+12-8n+1-3
Q: 6. Determine whether the following integral converges or diverges. dr VI!/3 + x
A: First we have to understand following concepts and tests to show convergence and divergence of given…
Q: 1 dx xln* (ex)
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Q: 10.Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.
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Q: Use the integral test to determine if E0n2e converges or diverge 3
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Q: - Show that sin converges. Hint: Use sinx <x for x 2 0.
A: Given: The series ∑n=1∞sin1n2, To show: The given series is convergent.
Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00
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Q: Show that the series f(x) =) Sinx/n Converges uniformly IR n=1 want to show f(x) = sin x/n converges…
A: We will use the basic knowledge of the theory of sequence and series of real-valued functions to…
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