Defining the limit
Limits are defined as being the values that a function or sequence "approaches" as the input or index approaches some value. They are y values observed, as x approaches a whole.
finding Limits by plugging in x values
The simplest method of solving limits algebraically is plugging in the value given if/when it is possible. This can be done with problems that are continuous, given that the direct substitution will not result in an undefined equation. Simply plug the value the limit is approaching where the x's are in the equation, and simplify to get your answer.
Check out the link below, for the answers to the practice problems to the left:
https://www.educreations.com/lesson/view/finding-limits-by-plugging-in-x-values/44832655/?s=v5x35R
Check out the link below, for the answers to the practice problems to the left:
https://www.educreations.com/lesson/view/finding-limits-by-plugging-in-x-values/44832655/?s=v5x35R
Factoring
These problems will be worked out step by step in this video:
https://www.educreations.com/lesson/view/factoring-limits/44832730/?s=6c6ubK |
Another way to evaluate limits algebraically is by factoring. You would factor a limit problem when the limit you are approaching cannot be plugged in because it would make the denominator equal zero. You factor the numerator and denominator of the expression (or either/or). When you get the same values, or factors, on the top and bottom of the fraction, you can cross them out to simplify. Then just plug in the value it's approaching to the x-value to find the solution.
Steps: 1) Factor out the numerator and denominator respectively. 2) Cross out the factors that the numerator and denominator both share. (This simplifies to 1) 3) Plug in the limit to the remaining x-value(s) |
Conjugate
For step by step breakdowns on how to solve these problems, go to
https://www.educreations.com/lesson/view/limits-conjugate/44832743/?s=va5k22
https://www.educreations.com/lesson/view/limits-conjugate/44832743/?s=va5k22
Common Denominator
L'Hopital's rule
L’Hopital’s Rule is one that states that if we have an equation in the indeterminate form of 0/0 or ∞/∞, all we must do is differentiate the numerator and denominator separately, and then take the limit as "x" approaches the given value.
Try to solve the problems below. Follow the link below to get the answers, and some further explanation:
https://www.educreations.com/lesson/view/l-hopital-s-rule/44832819/?s=1MiumL
Try to solve the problems below. Follow the link below to get the answers, and some further explanation:
https://www.educreations.com/lesson/view/l-hopital-s-rule/44832819/?s=1MiumL
End behavior
These problems will be worked out step by step in this video:
https://www.educreations.com/lesson/view/end-behavior/44835346/?s=4rnOIU
Continuity
Intermediate Value Theorem for Continuous Functions
Infinite Limits
For step by step solutions and additional information, visit the link below
Squeeze Theorem
Horizontal Asymptotes
For step by step solutions and additional information, visit the link below
https://www.educreations.com/lesson/view/horizontal-asymptotes/41937616/?s=8LDtT3&ref=app |