Need help with corrections.

Williian1

New member
Joined
Jan 13, 2021
Messages
1
Hi all,
So I understand for this question that f(6)=1 but I have troubles using that information with the f(6+h) part. Any clarification, guidance, examples, or just help in general would be greatly appreciated. Thanks!

For each of the following limits find the value or explain why it does not exist.

(i) lim β„Žβ†’0+ \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)
(ii) lim β„Žβ†’0βˆ’ \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)
(iii) lim β„Žβ†’0 \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)

Screen Shot 2021-01-13 at 11.46.52 AM.png
 

Subhotosh Khan

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Staff member
Joined
Jun 18, 2007
Messages
23,400
Hi all,
So I understand for this question that f(6)=1 but I have troubles using that information with the f(6+h) part. Any clarification, guidance, examples, or just help in general would be greatly appreciated. Thanks!

For each of the following limits find the value or explain why it does not exist.

(i) lim β„Žβ†’0+ \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)
(ii) lim β„Žβ†’0βˆ’ \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)
(iii) lim β„Žβ†’0 \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)

View attachment 24335
Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.
1610572777897.png
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
10,201
Hi all,
So I understand for this question that f(6)=1 but I have troubles using that information with the f(6+h) part. Any clarification, guidance, examples, or just help in general would be greatly appreciated. Thanks!

For each of the following limits find the value or explain why it does not exist.

(i) lim β„Žβ†’0+ \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)
(ii) lim β„Žβ†’0βˆ’ \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)
(iii) lim β„Žβ†’0 \(\displaystyle 𝑓(6+β„Ž)βˆ’π‘“(6)/h\)

View attachment 24335
Presumably you meant

(i) lim β„Žβ†’0+ [f(6+h)βˆ’f(6)]/h​
(ii) lim β„Žβ†’0βˆ’ [f(6+h)βˆ’f(6)]/h​
(iii) lim β„Žβ†’0 [f(6+h)βˆ’f(6)]/h​

Do you see why that is important?

For (i), sketch the segment whose slope is represented by the difference quotient; what will this look like as h approaches zero? Then do the same for (ii), and make a conclusion for (iii).
 
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