in the first lecture ..the professor mentioned more notations..f'=(df/dx)=(dy/dx) and that deltaY =delta F,then he wrote (Omits X0) what does that mean?? omits x0?? and in the example of f(x)=x^n ,n=1,2,3,..... find d/dx (x^n) he said that when we substitute in the main formula for computing derivative we won't use x0 ,instead we will just write x as we have no X floating around different from the X0 afterwards he said that x is fixed and delta x is moving so shouldn't there be an x0 for the initial point and x for the final one??

and please someone explain the Binomial theorem :)

Question

in the first lecture ..the professor mentioned more notations..f'=(df/dx)=(dy/dx)  and that deltaY =delta F,then he wrote (Omits X0) what does that mean?? omits x0??    and in the example of f(x)=x^n ,n=1,2,3,..... find d/dx (x^n)   he said that when we substitute in the main formula for computing derivative we won't use x0 ,instead we will just write x as we have no X floating around different from the X0   afterwards he said that x is fixed and delta x is moving so shouldn't there be  an x0 for the initial point and x for the final one??

and please someone explain the Binomial theorem  :)

anonymous · Answer

I didn't get the first question properly , but here's what I know :|dw:1377213568835:dw| here in my example I noted delta x with h, so when h->0 the value of the slope between the two points (the secant) goes to the value of the slope of the tangent we usually denote that by$$ \lim_{h \rightarrow 0} \frac{ \Delta y }{\Delta x  }= \lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h }=\frac{ dy }{ dx }$$