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Explanation & Answer
as we can see the grap that hthe roots of the quadratic are:
x1 = 3 and x2 = 3
The graph touch x axis at with y = 0 , so we got the roots in a twin roots number that is x = 3
Now, we can write our function for the quadratic as follows
f(x) = ( x - x1 ) ( x - x2 )
f(x) = ( x - 3 ) ( x - 3 )
f(x) = ( x - 3 ) ^2
f(x) = x^2 - 3x - 3x + 9
f(x) = x^2 - 6x + 9
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UCLA Limits Algebraic Limit Theorem Desired Inequality & Limit Theorem Worksheet
3. Let xn =
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3n+7 .
(a) Prove, directly using the definition, that limn→∞
xn =
2
3
.
(b) Prove, using the algebraic limit theorem, that limn→∞
xn =
2
3 8. (a) Let (xn) be bounded (not necessarily convergent) and assume that yn → 0 as
n → ∞. Show that xnyn → 0 as n → ∞. (Why can we not just use the Algebraic
limit theorem?)
(b) What about if yn → y as n → ∞ where y 6= 0?10. For the following, provide an example or prove that no such request is possible. You
may appeal to results from lectures.
(a) Sequences (xn) and (yn) which both diverge, but whose sum (xn + yn) converges.
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converges.
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Your troubleshooting and problem-solving skills were invaluable in ensuring that your colleagues and clients at Prevail PT were able to access the company’s wireless network on opening day at the new office. You soon discover that those skills are a way of life for the E-Communications Administrator. Today is proof of that. Just as you pour your morning coffee, you started receiving calls regarding cell phone connectivity issues to the router and Wi-Fi.You receive slack messages from the receptionist indicating that two clients are having connection issues with their phones.In speaking with the trainer, you discover that he is trying to connect to the router, not to the access point. How would you explain the problem to him and what directions would you give him for disconnecting from the router and connecting to the access point? Record the issue on the Documentation Form.The other client is having trouble using her cellular data and doesn’t want to use the guest wifi because she’s worried it’s not secure enough. Troubleshoot and document this issue and your solution for the client. Record the issue on the Documentation Form.(addtional question: In your office, where is your router located? Is it in your server room for security purposes or out in the open for closer proximity to users? How do you reconcile the needs of both proximity and security? please put addtional question in a individual word document)
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UCLA Limits Algebraic Limit Theorem Desired Inequality & Limit Theorem Worksheet
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(a) Prove, directly using the definition, that limn→∞
xn =
2
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UCLA Limits Algebraic Limit Theorem Desired Inequality & Limit Theorem Worksheet
3. Let xn =
2n+1
3n+7 .
(a) Prove, directly using the definition, that limn→∞
xn =
2
3
.
(b) Prove, using the algebraic limit theorem, that limn→∞
xn =
2
3 8. (a) Let (xn) be bounded (not necessarily convergent) and assume that yn → 0 as
n → ∞. Show that xnyn → 0 as n → ∞. (Why can we not just use the Algebraic
limit theorem?)
(b) What about if yn → y as n → ∞ where y 6= 0?10. For the following, provide an example or prove that no such request is possible. You
may appeal to results from lectures.
(a) Sequences (xn) and (yn) which both diverge, but whose sum (xn + yn) converges.
(b) Sequences (xn), which converges, and (yn), which diverges, but whose sum (xn+yn)
converges.
(c) A convergent sequence (xn), such that xn 6= 0 for all n ∈ N and (1/xn) diverges.
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