Find the Maclaurin series for the function. Use the table of power series for elementary functions shown
Question:
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below.
g(x) = arctan 5x
Transcribed Image Text:
POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)^(x − 1)² + ··· - 1 + x = 1x + ²x³ + x²-1³ +.. - - In x = (x - 1) et = 1 + x + sin x = x - cos x = 1 3! 2! arctan x = x = arcsin x = x + + +(-1) (x - 1)² (x-1)³ (x - 1)4 + 2 3 + 15 x7 5! 7! x4 4! 2.3 + 3 5 (1+x)= 1+ kx + The convergence at X = I 6! 15 x7 7 + + 5! 9! 18 8! 1.3x³ 2.4.5 k(k − 1)x² 2! + + + n! ±1 depends on the value of k. + (-1)"x²+1 (2n + 1)! + +. (-1)" x²n (2n)! 1.3.5x7 2.4.6.7 + k(k − 1)(k − 2)x³ 3! +. (-1)"x²n+1 2n + 1 · + +... (-1)"-¹(x-1)" n +... (2n)!x²n+1 (2"n!)²(2n + 1) ++ + . k(k-1) (kn+1)x + n! Interval of Convergence 0 < x < 2 -1 < x < 1 0 < x≤ 2 -∞0 < x < ∞0 -∞0 < x < ∞0 -∞0 < x < 00 -1 ≤ x ≤ 1 -1 ≤ x ≤ 1 -1 < x < 1*
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 88% (9 reviews)
To find the Maclaurin series for the function gx arctan5...View the full answer
Answered By
Mary Boke
I have teached the student upto class 12th as well as my fellow mates.I have a good command in engineering,maths and science.I scored 90+ marks in 10th and 12th in maths.
0.00
0 Reviews
10+ Question Solved
Related Book For
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards
Question Posted:
Students also viewed these Mathematics questions
-
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below. f(x) = e 6x POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x 1)(x - 1) +...
-
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below. f(x) = sin 5x POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x 1)(x - 1)...
-
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below: f(x) = cos 2 x POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)(x -...
-
Steven Stores, Inc. provided the following statement of net income for the current year. All income is subject to a 40% income tax rate. The company also had $ 735 of unrealized holding gains on its...
-
1. Which of the following statements about due diligence is false? a. It is designed to ensure the legitimacy of securities offered to the public. b. It is designed to ensure that there is no...
-
Opal, age 75, has a $100,000 ordinary life insurance policy that has a cash value of $35,000. Opal is concerned about the cost of long-term care in a nursing home. A new agent of a national life...
-
Fun-Tastic Shows, Inc., is a company that hosts carnivals and similar events. Susan Swartwood, Crystal Groth, and a minor (named in the case as M.G.S.) attended Fun-Tastics Rhododendron Festival in...
-
Janice Sanders, CEO of Pine Crest Medical Clinic, is concerned over the number of times patients must wait more than 30 minutes beyond their scheduled appointments. She asked her assistant to take...
-
Data manipulation language (DML) provides a number of capabilities that allow you to build custom queries of existing data. What are two capabilities you might use to limit the data you select or...
-
Find the sum of the convergent series. [(3) n=0 1 (n + 1)(n + 2)]
-
Find the interval of convergence of the power series. 18 n=0 (-1) xn n!
-
Assume that the comparable worth remedy for wage discrimination against women will require governmental and large private employers to increase the wages they pay to women in female dominated jobs....
-
Short essay question. From the material above and the data from the document it is clear that Social Security benefits are progressive. That is those whose average earnings are low receive a higher...
-
Prove that () = ; [Let z = a + bi and z = c + di]
-
answer the next question. Mass spectrometers are used in archaeological studies to help date ancient artifacts. The relative amounts of carbon-12 and carbon-14 isotopes in a sample of organic...
-
Why would companies choose one method of accounting for Depreciation over another method?What are the benefits of each depreciation type?
-
Does demoing boost sales during the demoing period? b. If so, is the boost temporary, or does demoing boost sales beyond the demoing period? c. Do the endcap display contests boost sales.
-
Fifty numbers are rounded off to the nearest integer and then summed. If the individual roundoff errors are uniformly distributed over (.5, .5), approximate the probability that the resultant sum...
-
Gopher, Inc. developing its upcoming budgeted Costs of Quality (COQ) with the following information: Expense Item Budget Raw Materials Inspection $ 15,000 EPA Fine 200,000 Design Engineering 15,000...
-
Describe and sketch the surface. y = /2 24
-
Determine whether the planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection. 5x 3y + z = 4 x + 4y + 7z = 1
-
Prove the property of the cross product. u v = 0 if and only if u and v are scalar multiples of each other.
-
Justine is studying at TAFE NSW in Sydney. She discovers that there is $2 million dollars in her bank account. She presumes that the bank has made an error. Justine has been a problem gambler for...
-
Assume that you work for an organization that is interested in expanding solar energy use nationwide. Your organization is interested in promoting legislation that will generate and increase...
-
Webster University has plans to build on land that is now used as wetlands and a drainage basin for rainwater near its St. Louis campus. Webster University contracted an environmental survey of the...
Study smarter with the SolutionInn App