LIMITS
INTRODUCTION
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.
EXPLANATION
EXAMPLE
1. Replacing the value of x by its tendency (when x tends to a number)
(x2 − 1) (x − 1)
Let's work it out for x=1:
(12 − 1) (1 − 1) = (1 − 1) (1 − 1) = 0 0
2. Factoring
By factoring (x2−1) into (x−1)(x+1) we get: | |
![]() | |
Now we can just substitiute x=1 to get the limit: | |
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3. Conjugate
When it's a fraction, multiplying top and bottom by a conjugate might help.
![]() | Evaluating this at x=4 gives 0/0, which is not a good answer! |
Multiply top and bottom by the conjugate of the top: | ![]() | |
Simplify top using ![]() | ![]() | |
Simplify top further: | ![]() | |
Cancel (4−x) from top and bottom: | ![]() |
![limit as goes to 4 of (2-sqrt(x))/(4-x) = limit as x goes to 4 of 1/(2+sqrt(x)) = 1/4](https://www.mathsisfun.com/calculus/images/lim-conjugate-6.png)
VIDEO
Here is a video for you to understand better this topic
PRACTICE
[Solution]
[Solution]
GOOD LUCK AND HOPE YOU HAVE UNDERSTOOD!!
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