When you want to solve calculus problems such as derivatives and limits you must have knowledge about algebra. If you want to take the limit of some function you will need to find the value of the variable in that function.
Constants and Polynomials
Limits are always written in the graphic of function. For instance, you will have ’’the limit of f(x) as x approaches c’’. This will require the knowledge about polynomials. Limit of a constant value of x will always be the constant which means that this will never change. When we have polynomials, the limit of function will be defined at the x approaches.
When we have complex functions they can easily be solved with the limit operations. We must know some rules such as:
- limit of a sum = sum of the limits
- limit of a product = product of a limits
For these rules you will use subtraction and division.
For this we have two basic rules:
- if denominator is infinitely large, limit will be zero
- if numerator is infinitely large, limit can be positive or negative infinity
This is because the x will never reach the value that is defined to be approaching.
Disruptions or discontinuity in the functions occurring when the denominator of a function is equal to zero. You can bypass this if multiply through the numerator and denominator by a factor that removes that discontinuity.
When you do limits you can check the continuity of a function at some point. If you go from that point to the left, and after that to the right, and if limit is equal at each side that means that this function is continuous at that point. If it is not equal from both sides, left and right, that means that function is discontinuous at that point.