a) lim (0 Scratch worki < क n < ε ( <ε² < not Proof: Let eso, By the archmedian a natural number N°(E) >o property , there exist So N(E) > N(E) we have n> ½ ₂. For all then ε > 1 nti b) Scratch work: = In < EL We can rewrite "this as. บท n+1 √n> ૮૬ √n रह ९० 10/48 lim (√n² + 1 n ) = 0 -n-c | |< -n - √n² n> √ Proof: Let & xo, by the archimedian property, there exist a 'N(e) >o where N(E). natural member For all n = N(E), we know n > Jes then E therefore > √n²+1 -n. Thus 11m (√571-n)=0. I'm √n²+1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 56E
icon
Related questions
Question

Can an expert please look over my work and see if i solve the problemss correct. If it is wrong please provided and explanation on why so i can understand it please. Thank you!

"USE THE DEFINITION OF THE LIMIT OF A SEQUENCE TO ESTABLISH THE FOLLOWING LIMITS"

PART A AND B R SOLVED BELOW.

a) lim (0
Scratch worki
<
क
n
< ε
(
<ε²
<
not
Proof: Let eso, By the archmedian
a natural number N°(E) >o
property
, there exist
So N(E) >
N(E) we have n> ½ ₂.
For all
then ε > 1
nti
b)
Scratch work:
=
In
<
EL
We can rewrite "this as.
บท
n+1
√n>
૮૬
√n
रह ९०
10/48
lim (√n² + 1 n ) = 0
-n-c
| |<
-n
-
√n²
n> √
Proof: Let & xo, by the archimedian property, there exist a
'N(e) >o where N(E).
natural member
For all
n = N(E), we
know n >
Jes then
E therefore
> √n²+1 -n. Thus
11m (√571-n)=0.
I'm
√n²+1
Transcribed Image Text:a) lim (0 Scratch worki < क n < ε ( <ε² < not Proof: Let eso, By the archmedian a natural number N°(E) >o property , there exist So N(E) > N(E) we have n> ½ ₂. For all then ε > 1 nti b) Scratch work: = In < EL We can rewrite "this as. บท n+1 √n> ૮૬ √n रह ९० 10/48 lim (√n² + 1 n ) = 0 -n-c | |< -n - √n² n> √ Proof: Let & xo, by the archimedian property, there exist a 'N(e) >o where N(E). natural member For all n = N(E), we know n > Jes then E therefore > √n²+1 -n. Thus 11m (√571-n)=0. I'm √n²+1
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell