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JingleBells
 3 years ago
Problem Set 1: 1D10
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JingleBells
 3 years ago
Problem Set 1: 1D10 Show that

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JingleBells
 3 years ago
Best 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 \[f \prime(a) exist\]

JingleBells
 3 years ago
Best ResponseYou've already chosen the best response.0I 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...

JXP
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, 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!

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

JingleBells
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks 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.
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