Started basics of calculus as a high school student , and Limits already confuse me . Can somebody explain it to me why limits actually work .If the value of x tends to infinity ,which is undefined then how we can find out the exact value of the function?
Like , in differentiation , after taking the limit, h approaches to 0 , but h cannot be zero , but after removing it from denominator we take it as 0? How does that even work and how it does not affects our actual answer?
Also while calculating the area of a circle . Is it approximatelyπr² or exactlyπr²?Even if we sliced the circle in infinite parts , there are always some irregularities for it to be a parllelogram , So πr² should be approximation?
Basically , why do limits work so well ? I dont get the logic and mechanism behind them. Help real confused here, Please someone explain to me like I am a kid.