1a, The two theorems are equivalent, and whichever one is easy
to use for a particular problem, we use that one. Do you use Root
or Ratio test for 
1b, How do you find the radius of convergence of 
1c, the function 
61 n=1 (n+1)"
(2n)r2n 00 n-1 n!
f (a) 1 1-r
2-x () b
Homework Answers
Add Answer to:
1a, The two theorems are equivalent, and whichever one is easy to use for a particular problem, we use that one. Do you...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of f(x) at x = -5. (a) The nth derivative of f(x) is f(n)(x) = At r = -5, we get f(n)(-5) = (c) The Taylor series at r = -5 is +00 T(x) = { (3+5)" n=0 = (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+too an and so its radius of convergence is R= |x...
(35 pls) Determine if each of the following seven series converge or diverge. Do not use...
(35 pls) Determine if each of the following seven series converge or diverge. Do not use a test for convergence or a test for divergence more than once. If you use the Integral Test, do not bother to show me that you checked the three prerequisites to that test. i) 2(04-) n.1 ii) (-1)"n(2n)! -1 (n + 1) (2n) 21 n=1 n 3 iii) 2+ n-1 iv) n=0 1+en 00 1 v) n-07T +n* vi) (-1)"e" 1+en n=0 vii) Ž(-1)"...
Question # 2. (2 marks) Show that the ratio test fails to apply to the series,...
Question # 2. (2 marks) Show that the ratio test fails to apply to the series, 7-n+(-1)", but that the root test does apply. Use the root test to determine if the series converges or not. n=0 Question # 3. (3 marks) Consider the power series, f(x) = į an(x + 1)". Suppose we know that f(-4), as a series, diverges, while f(2) converges. Determine the radius of convergence of the power series for f'(x). Precisely name the results we...
Given § (-1)" (n=1)". Which test would you use to determine the convergence or 10 divergence...
Given § (-1)" (n=1)". Which test would you use to determine the convergence or 10 divergence of this series? Integral Test Ratio Test Root Test Comparison Test
To test the series e 2n for convergence, you can use the Integral Test. (This is...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
Use the Root Test to determine the convergence or divergence of the series. (If you need...
Use the Root Test to determine the convergence or divergence of the series. (If you need to use co or -oo, enter INFINITY or -INFINITY, respectively.) (2017)." n = 1 lim janl = n → 00 O converges o diverges O inconclusive
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent....
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent. 2. (2 points) Determine whether the series - (Use cos n<1 for all n) 3. (3 points) Test the series -1) 3 for absolute convergence. (Use the Ratio Test) 2n +3) 4. (3 points) Determine whether the series converges or diverges. 3n +2 n-1 (Use the Root Test) 5. (3 points) Find R and I of the series (z-3) 1 Find a power series...
Can you please so (a&b) from #2 and (b&e) from #1 2. Use the ratio test or the root test to find the open interval in which the series converges. No need to test for the end-point. (a) ζ...
Can
you please so (a&b) from #2 and (b&e) from #1
2. Use the ratio test or the root test to find the open interval in which the series converges. No need to test for the end-point. (a) ζ는 34-1-1 (b) 2 (-5)n+1 3n+2(n2 +1) Name: 1. Determine the convergence (absolute or conditional) of the given series. (-1)P ndentI n= 1 1. Determine the convergence (absolute or conditional) of the given series. (e) Ση3e_n2
2. Use the ratio test or...
Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor'...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's r...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of f(x) at x = -5. (a) The nth derivative of f(x) is f(n)(x) = At r = -5, we get f(n)(-5) = (c) The Taylor series at r = -5 is +00 T(x) = { (3+5)" n=0 = (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+too an and so its radius of convergence is R= |x...
(35 pls) Determine if each of the following seven series converge or diverge. Do not use a test for convergence or a test for divergence more than once. If you use the Integral Test, do not bother to show me that you checked the three prerequisites to that test. i) 2(04-) n.1 ii) (-1)"n(2n)! -1 (n + 1) (2n) 21 n=1 n 3 iii) 2+ n-1 iv) n=0 1+en 00 1 v) n-07T +n* vi) (-1)"e" 1+en n=0 vii) Ž(-1)"...
Question # 2. (2 marks) Show that the ratio test fails to apply to the series, 7-n+(-1)", but that the root test does apply. Use the root test to determine if the series converges or not. n=0 Question # 3. (3 marks) Consider the power series, f(x) = į an(x + 1)". Suppose we know that f(-4), as a series, diverges, while f(2) converges. Determine the radius of convergence of the power series for f'(x). Precisely name the results we...
Given § (-1)" (n=1)". Which test would you use to determine the convergence or 10 divergence of this series? Integral Test Ratio Test Root Test Comparison Test
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
Use the Root Test to determine the convergence or divergence of the series. (If you need to use co or -oo, enter INFINITY or -INFINITY, respectively.) (2017)." n = 1 lim janl = n → 00 O converges o diverges O inconclusive
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent. 2. (2 points) Determine whether the series - (Use cos n<1 for all n) 3. (3 points) Test the series -1) 3 for absolute convergence. (Use the Ratio Test) 2n +3) 4. (3 points) Determine whether the series converges or diverges. 3n +2 n-1 (Use the Root Test) 5. (3 points) Find R and I of the series (z-3) 1 Find a power series...
Can
you please so (a&b) from #2 and (b&e) from #1
2. Use the ratio test or the root test to find the open interval in which the series converges. No need to test for the end-point. (a) ζ는 34-1-1 (b) 2 (-5)n+1 3n+2(n2 +1) Name: 1. Determine the convergence (absolute or conditional) of the given series. (-1)P ndentI n= 1 1. Determine the convergence (absolute or conditional) of the given series. (e) Ση3e_n2
2. Use the ratio test or...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1
Question 2 (10 marks) In this question you must state if you use any...
Most questions answered within 3 hours.
-
Below is the trial balance of Tom’s Tents at 5 April 2018.
£
£
Trading account:...
asked 5 minutes ago -
For this question, we want to implement the basic
java classes to support the concept of an...
asked 6 minutes ago -
Two random variables X and Y have joint density function f(x,y)
=c(where c >0 denotes an...
asked 8 minutes ago -
Bonita Corporation issued 1,900 shares of $10 par value common
stock upon conversion of 950 shares...
asked 13 minutes ago -
When finding confidence interval for mu , if population standard
deviation (sigma) is known, we use...
asked 43 minutes ago -
Convert your enthalpy of reaction (kJ/mol) to heat of explosion
(kJ/kg) using the molar mass of...
asked 28 minutes ago -
At what annual rate would the following have to be
invested?
$8,929, to grow to $55,581,...
asked 27 minutes ago -
If the codon were 5 bases long instead of three, how many codons
would exist in...
asked 34 minutes ago -
Mittuch Corp. is evaluating a project with the following cash
flows. The company uses a discount...
asked 41 minutes ago -
An income elasticity coefficient of −1.8 means the product is a
normal good.
true or false
asked 34 minutes ago -
PLEASE ANSWER ASAP ASIAN AMERICAN HISTORY
Considering the number of migrants and the time period in...
asked 41 minutes ago -
1. If a good has a price elasticity of demand equal to
0, ________.
a) the...
asked 44 minutes ago