Reference no: EM13910636
1. Find the interval and radius of convergence for the following two power series
a. n=1Σ∞ 2nxn/n!
b. n=1Σ∞ (x-3)n/2n+1
2. Find the third Taylor polynomial for f (x)= tanx centered at a = π/4.
3. a. Find the third Taylor polynomial for f (x) = sin x centered at π
b. What is the bound on the error if we use the Taylor polynomial from part a. to approximate sinx for
π- ¼ ≤ x ≤ π ≤ +1/4.
4. Use the Maclaurin series for tan-1x to approximate 0∫5 tan-1x2 dx with an error less than .001.
5. Give series representations (and their radius' of convergence) for the following functions, using known series:
a. x/3-x
b. 1/(3-x)2
c. ln(1 + x2)(start with 1/1+x)
6. Use the series you obtained in problem 5 c. to approximate 0∫1/2 ln(1+ x2)dx with an error less than .001.
7. Let f(x)= √(x+1)
a. Find T2 , the second Taylor polynomial for f(x) centered at a = 0.
b. Get a bound for the error if we assume 0 <x < ½.
|
The number of patients seen by the two doctors
: In a situation similar to one you may have seen before, there is a clinic with two physicians, Dr. X and Dr. Y, and each doctor can be scheduled to see at most 3 patients per hour. The joint probability mass function is given by the following table. ..
|
|
Find the probability that a randomly selected us bank
: Find the probability that a randomly selected U.S. bank will have a net interest margin that exceeds 5.40 percent. Find the probability that a randomly selected U.S. bank will have a net interest margin less than 4.40 percent.
|
|
Company''s current hiking shoe design lasts
: It is well established that your company's current hiking shoe design lasts on average 900 miles. It is also well known that the durability of hiking shoes is normally distributed. By adding a new ingredient to the soles, you believe you can extend t..
|
|
Molarityof a naoh solution
: What is the molarityof a NaOH solution if 15.5 mL of a 0.220 M H2SO4 solution is required to neutralize a 25.0 mL sample of the NaOH solution?
|
|
Find the interval and radius of convergence
: Find the interval and radius of convergence for the following two power series - n=1Σ∞ 2nxn/n!
|
|
Describe the statistic formula used
: Describe the statistic formula used here and breakdown how
|
|
Population standard deviation
: Suppose a population has a population standard deviation of 50-What would be the upper limit of a 88 percent-confidence interval if you obtained a sample of size 60 that had a sample mean of 1000-1010-0-1007-6-1058-7
|
|
What is the probability
: In an undergraduate statistics class of 80,10 of the students are,actually, graduate students.If 5 students are chosen at random from the class, what is the probability
|
|
Calculate the probability that fewer of randomly selected
: Calculate the probability that 45 percent or fewer of 400 randomly selected German adults would have purchased blue jeans in the past three months.
|