Question

Can someone please explain the solution to question 1C-2 in Problem Set1? Thanks a million

Answer 1

You may see the attached pdf. If you have any questions just tell me.

Answer 2

@joht, your solution makes a LOT of sense to me. I didn't initially understand the solution from the answer key, but after reading your logic, I see how simple the answer is. Well done!

Initially I misread the question and thought it was asking to prove that f'(x) = g(x) for all x, but now I see that it was asking f'(a) = g(a) where x = a.

Another way to look at it is by performing the chain rule (although this doesn't answer the question).

Hope I didn't just hijack the thread, but wanted to let the OP know what initially caused my confusion in case they had a similar misunderstanding.

Answer 3

Thanks for the help. @joht, your solution made it a lot more clear and @datanewb, your explanation also helped. However, I still don't quite understand the final step: how the limit of x tends to a of g(x) is equal to g(a). Where does g(a) come from? I think my problem is that I don't really understand the question

Answer 4

Imagine an example for g(x). Lets say \[g(x)=x^2\] Then \[ \lim_{x \rightarrow α} {g(x)} =\lim_{x \rightarrow α} x^{2} = α^{2} = g(α) \]. The symbol g(α) says just that: Put the certain number α in place of x.

Answer 5

Thanks :), makes sense