Need help with corrections.

[Williian1]

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 _ℎ→0⁺ \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)
(ii) lim _ℎ→0⁻ \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)
(iii) lim _ℎ→0 \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)

 

[Subhotosh Khan]

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 _ℎ→0⁺ \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)
(ii) lim _ℎ→0⁻ \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)
(iii) lim _ℎ→0 \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)

View attachment 24335

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

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 _ℎ→0⁺ \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)
(ii) lim _ℎ→0⁻ \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)
(iii) lim _ℎ→0 \(\displaystyle 𝑓(6+ℎ)−𝑓(6)/h\)

View attachment 24335

Presumably you meant

(i) lim ℎ→0+ [f(6+h)−f(6)]/h​

(ii) lim ℎ→0− [f(6+h)−f(6)]/h​

(iii) lim ℎ→0 [f(6+h)−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).