Question

the exponential function that can be described as e^x = (1 + x/n)^n in the limit...

the exponential function that can be described as e^x = (1 + x/n)^n in the limit as n -> infinity through positive integers. calculate approximation to e^(i pi) by choosing n=10. Make sure you write down the values of (i pi)/n and (1 + (i pi)/n) as well as your final answer of (1 + (i pi)/n)n. How close is your answer to -1?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
:The exponential function f(x) = e x dominates any ”power of x” function as x increases...
:The exponential function f(x) = e x dominates any ”power of x” function as x increases to infinity. That is lim x k e x = 0 for every positive value k. Use the power series given below to verify this fact. e x = 1 + x + x 2 2! + x 3 3! + x 4 4! + x 5 5! + ...
Consider the following exponential probability density function. f(x) = (1)/(5)e−x/5    for x ≥ 0 (a) Write...
Consider the following exponential probability density function. f(x) = (1)/(5)e−x/5    for x ≥ 0 (a) Write the formula for P(x ≤ x0). (b) Find P(x ≤ 3). (Round your answer to four decimal places.) (c) Find P(x ≥ 5). (Round your answer to four decimal places.) (d) Find P(x ≤ 7). (Round your answer to four decimal places.) (e) Find P(3 ≤ x ≤ 7). (Round your answer to four decimal places.)
sketch a neat, piecewise function with the following instruction: 1. as x approach infinity, the limit...
sketch a neat, piecewise function with the following instruction: 1. as x approach infinity, the limit of the function approaches an integer other than zero. 2. as x approaches a positive integer, the limit of the function does not exist. 3. as x approaches a negative integer, the limit of the function exists. 4. Must include one horizontal asymtote and one vertical asymtote.
(a) Show that the function f(x)=x^x is increasing on (e^(-1), infinity) (b) Let f(x) be as...
(a) Show that the function f(x)=x^x is increasing on (e^(-1), infinity) (b) Let f(x) be as in part (a). If g is the inverse function to f, i.e. f and g satisfy the relation x=g(y) if y=f(x). Find the limit lim(y-->infinity) {g(y)ln(ln(y))} / ln(y). (Hint : L'Hopital's rule)
Write a function called TaylorSin.m that takes as input an array x, and positive integer N,...
Write a function called TaylorSin.m that takes as input an array x, and positive integer N, and returns the Nth Taylor polynomial approximation of sin(x), centered at a = 0. The first line of your code should read function s = TaylorSin(x,N) HINT: in computing k!, use kfact = k*(k-1)*kfact since you are counting by 2
1. Find T5(x): Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0. T5(x)=   Using...
1. Find T5(x): Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0. T5(x)=   Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.00054 of the right answer. Assume for simplicity that we limit ourselves to |x|≤1. |x|≤ = 2. Use the appropriate substitutions to write down the first four nonzero terms of the Maclaurin series for the binomial:   (1+7x)^1/4 The first nonzero term is:     The second nonzero term is:     The third...
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a...
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a general term (as a function of the variable n) for the sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…} an= Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. (If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer...
Sigma n=1 to infinite (-1)^n sin(pi/n) I confuse about this alternative test I know this function...
Sigma n=1 to infinite (-1)^n sin(pi/n) I confuse about this alternative test I know this function F(x) = sin(pi/n) should be decreasing for all n value. but it is not decreasing when n =1 , n=2 but the answer is convergent. so how I figure out this one, is it okay to ignore when n is 1 or 2? then why? cause the condition said, Function must be decreasing for all n value.
Problem 1: Find a non-zero function f so that f'(x) = 3f(x). The exponential function f(x)...
Problem 1: Find a non-zero function f so that f'(x) = 3f(x). The exponential function f(x) = e^x has the property that it is its own derivative. (d/dx) e^x = e^x f(x) = e^(3x) f '(x) = e^(3x) * (d/dx) 3x = e^(3x) * 3 = 3e^(3x) = 3 f(x) Problem 2: Let f be your function from Problem 1. Show that if g is another function satisfying g'(x) = 3g(x), then g(x) = A f(x) for some constant A????
1.)Find T5(x), the degree 5 Taylor polynomial of the function f(x)=cos⁡(x) at a=0. T5(x)=   Find all...
1.)Find T5(x), the degree 5 Taylor polynomial of the function f(x)=cos⁡(x) at a=0. T5(x)=   Find all values of x for which this approximation is within 0.003452 of the right answer. Assume for simplicity that we limit ourselves to |x|≤1. |x|≤ 2.) (1 point) Use substitution to find the Taylor series of (e^(−5x)) at the point a=0. Your answers should not include the variable x. Finally, determine the general term an in (e^(−5x))=∑n=0∞ (an(x^n)) e^(−5x)=  +  x +  x^2 +  x^3 + ... = ∑∞n=0...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT