question 49 please quickly thanks !!! 49. Let {r„}ı be a sequence of real numbers such that x, →1.Calculate lim,,→∞ exp(cos(xn – 1) – 1). (Proof is not required)

Answered: Image /qna-images/answer/a9c7c974-aaea-41ce-aa7f-55db99216545.jpg

Answered: 49. Let {x,}=1 be a sequence of real…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 74E

See similar textbooks

Similar questions

Prove the conjecture made in the previous exercise.
Suppose that {xn} is a sequence of real numbers satisfying lim (as n→∞) xn = 1. prove that lim (as n→∞) (1 + 2xn) = 3.
1. Consider the sequence Xn = √n + 1 − √n, n ≥ 1. Prove that (xn)n isconvergent. Find its limit.
Define the sequence {Sn} by Sn= [ 1 / (2)(1) ] + [ 1 / (3)(2) ] + ............. + [ 1 / (n+1)(n) ] Prove that Limn→∞ Sn = 1.
Let n be a positive integer. For which n are the two infinite one-sided limits limx→0±1/xn^n equal?
(i) Let gn(x) =1/n(1 + x2) For any fixed x ∈ R, we can see that limgn(x) = 0 so that g(x) = 0 is the pointwise limit of the sequence (gn) on R. Is this convergence uniform? The observation that 1/(1 + x2) ≤ 1 for all x ∈ R implies that .
Suppose that F(u) denotes the DFT of the sequence of f(x)={1, 2, 3, 4}? What is the value of F(14)? (Hint: DFT periodicity)
Suppose that {xn} is a sequence of real numbers satisfying lim (as n→∞) xn = 1. prove that lim (as n→∞) (1 + 2xn) = 3. prove this don't calculate limit.
Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s.
1. Use the definition of the limit ( epsolon - delta ) to show thatlim of 1/z as z approaches -i2. Give the condition which ensure that |ez| < 1 where z in C.
If (an) has limit −1 and (bn) tends to infinity, does it follow that only finitely many terms of (anbn) are positive?
Prove that the sequence {cn} converges to c if and only if the sequence {cn- c} converges to 0.

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS

49. Let {x,}=1 be a sequence of real numbers such that xn Calculate lim,∞ exp(cos(x, – 1) – 1). (Proof is not requi