Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

JingleBells Group TitleBest ResponseYou've already chosen the best response.0
\[g(h)=\left[ f(a+h)f(a) \right]/h\]has a removable discontinuity at h=0 \[f \prime(a) exist\]
 2 years ago

JingleBells Group TitleBest ResponseYou've already chosen the best response.0
I gave it a try, is anyone convinced? \[g(0^{})=\lim_{h \rightarrow 0}\left[ f(a+h)f(a) \right]/h=f \prime (a)\] \[g(0^{+})=\lim_{h \rightarrow 0}\left[ f(a+h)f(a) \right]/h=f \prime (a)\] Since the lefthand limit=righthand limit at h=0, i.e. \[f \prime(a)=f \prime(a) \] Therefore f'(a) exists and g(h) has a removable discontinuity at h=0 Sounds about right? seems too simple an answer...
 2 years ago

JXP Group TitleBest ResponseYou've already chosen the best response.0
Yes, it is correct. The first problem set goes over some basics of high school calculus since some of the students have not taken calculus yet. So keep on going if you're fairly confident with your answer!
 2 years ago

Stacey Group TitleBest ResponseYou've already chosen the best response.0
What you have is correct. It is removable because by defining g(0) = f'(a) the function becomes continuous at h=0.
 2 years ago

JingleBells Group TitleBest ResponseYou've already chosen the best response.0
Thanks a million! I'm using these videos to prepare for Alevels so I'm bound to be out of my depth most of the time.
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.