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 one year 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?
 one year 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
 one year 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.

hemn
 one year 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 \[xx_0\]

fantastic001
 one year 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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