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anonymous
 3 years ago
Basic question: In the 2nd lecture on the use of limits for proving continuity of differentiable functions, is lim { [f(x)  f(x0)]/[xx0] } = 1/[xx0] lim [f(x)  f(x0)] if we see lim as an operator?
anonymous
 3 years ago
Basic question: In the 2nd lecture on the use of limits for proving continuity of differentiable functions, is lim { [f(x)  f(x0)]/[xx0] } = 1/[xx0] lim [f(x)  f(x0)] if we see lim as an operator?

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Waynex
 3 years ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow x_{0}} \left( \frac{ f(x)f(x_{0}) }{ xx_{0} } \right) = \frac{1}{xx_{0}} \lim_{x \rightarrow x_{0}} \left( f(x)f(x_{0}) \right)\] If you are asking if the right hand side represents a valid algebraic manipulation of the left hand side, the answer is no. In the denominator, x is not a constant; therefore, it cannot be moved out of the limit.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0no you can not consider it as an operator. however, it is more beneficial to [/delta x/] instead of \[xx_0\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0x > x0, then f(x)  f(x0) is changing but also x  x0 is changing therefore you cannot treat xx0 as constant and put it before limit
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