can any one explain me how limits actiually works ....!!?

Question

i want to know how limits work with given function ,....

similar to   if weadd2+3 we get five ....

ijust wnt that nmuch deep answere

 

Answer 1

I think one of the neatest uses of limits is calculating the slope of the tangent line to a curve f(x) to do this we  calculate the value of the function at x+h which is f(x+h) then we subtract the value at x f(x) and then we divide the difference by h and then take the limit as h approaches 0

 

            slope=limit_h→0 {f(x+h)-f(x)}/h  to give you a specific example suppose f(x)=x²

            then slope = limit_h→0((x+h)²-x²)/h = limit_h→0(x²+2hx+h²-x²)/h=limit_h→0(2x+h)=2x

So the slope of the tangent line to the parabola y=x² is 2x and is an example of a limit actually works.

 

Hope this helps somewhat.

Jim