Convergence parameter Find the values of the parameter p > 0 for which the following series converge.
72.
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)
Additional Math Textbook Solutions
Glencoe Math Accelerated, Student Edition
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus and Its Applications (11th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus & Its Applications (14th Edition)
- Fpr the convergent series from 1 to infinity of ((-1)^k*k)/(k^2+1), what is the value of the series with a remainer less than 10^-3 (an estimate)arrow_forwardFind a power series solution of the differential equation given below. Determine the radius of convergence of the resulting series, and use the series given below to identify the series in terms of familiar elementary functions.arrow_forwardNumerical Methods Use 5 decimal place mantissa. Approximate the following functions using Taylor series. Solve the absolute and relative error in each item when x = 3(Answer Problem No.3)arrow_forward
- Using power series with integration to find the length of x^2/a^2+y^2/b^2=1. assume b>0. Solution hint as below: consider there two case(a>b, or a<b) with different solution Set x=acosu,y=bsintu,0<=u<=2pi, L=integral(2pi,0()sqrt((dx/du)^2+(dy/dt)^2)dtarrow_forwardDoes the series (showing the picture) converge or diverge? Choose the correct answer below. 1) The integral test shows that the series converges 2) The nth-term test shows that the series converges 3) The series diverges because the series is a geometric series with |r|>=1 4) The nth-term test shows that the series divergesarrow_forwardtaylor series & radius of convergence of f(x)=sin(2x), centered at a= pi (22/7)arrow_forward
- Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu a)Find the Taylor series generated by g(x) = 1/√x centered at 1. Include information about its radius of convergence b)Find the Maclaurin series generated by f (x) = 1/3^√(1 + x). Include information about its radius of convergence.arrow_forward2. Find the interval of convergence for the Maclaurin series for the function of f(x)= sin(x) a) Find the Maclaurin series for sin(x): b) Apply the Ratio Test: (Form the fraction |an+1| / |an| and simplify as much as possible) c) Evaluate the limit: d) Find the interval of convergence: HINT: Recall that the limit needs to be less than 1arrow_forwardi need solution very very quickly please #complex analysis# Where does each of the following series in pictures converge uniformly: hint: use ratio test , comparison test ,Weierstrass M-Test, in solutionarrow_forward
- Sigma k=1 to infinity -20*8^k/4*9^k series converges or diverges. show stepsarrow_forwardExamine the convergence of the given series. (image) Attempt 1: Let's try the Divergence Test: General term for the positive part of the series: un=? Limit of this: limn→∞un= limn→∞un ....?.... (equal to 1, not equal to 1, not equal to 0, not equal to 0) According to the n-term test for Divergence, ....?..... (convergent or divergent) Attempt 2: Let's try the Alterne Serial test: Calculate the derivative: d/dn un=? d/dn un ...?... (Less than 1, greater than 1, less than 0, greater than 0, changes sign) since the series ...?... (monotonically increasing, monotonically decreasing, non-monotonic) According to alterne series test ....?.... (convergent or divergent) Absolute Convergence: As a result of these two trials, we can say the following for absolute convergence: ∞∑n=3 (−1)n+1 (ln(2n)/7n) series ...?... (conditionally convergent, absolutely convergent or divergent)arrow_forwardUsing Taylor's series. find the value of the following: a. f(x)=sin 3x at x=0.4 b. for the function of x4+x-2 centered a=1arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning