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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
 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
 one year ago

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WaynexBest 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.
 one year ago

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

fantastic001Best ResponseYou've already chosen the best response.0
x > 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
 10 months ago
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