- #1
Agreed. Some of the explanation near the end of your image falls apart for me, but the method is clear. The function in original form, and in the simplified form is not permitted to accept x=5, but the LIMIT can still be found. However near to x=5 we choose, (x-5)/(x-5) will still be equal to 1 ; and so the limit will be (x+3)=(5+3)=8.marciokoko said:I'm taking an online coursera course and the guy is explaining limits.
He doesn't really explain why he does this numerator thing.
Limits represent the value that a function approaches as the input variable gets closer to a specific value. In science, limits are important because they help us understand the behavior of a function and make predictions about its output. They also allow us to analyze the behavior of systems and make accurate conclusions about real-world phenomena.
Limits help us understand the behavior of a function by telling us what happens to the output of the function as the input variable gets closer and closer to a specific value. This can help us determine the overall trend or pattern of the function, whether it is increasing, decreasing, or approaching a certain value. Limits also allow us to identify any potential discontinuities or singularities in the function.
There are three main types of limits: one-sided limits, two-sided limits, and infinite limits. One-sided limits involve approaching a specific value from either the left or right side, while two-sided limits involve approaching from both sides. Infinite limits occur when the output of a function approaches positive or negative infinity as the input variable approaches a certain value.
Limits are closely related to derivatives, as the derivative of a function at a specific point is defined as the limit of the function as the input variable approaches that point. This means that limits help us understand the instantaneous rate of change of a function, which is essential in many scientific fields such as physics, chemistry, and economics.
Yes, limits can help us find the maximum or minimum value of a function. By taking the limit of a function as the input variable approaches infinity or negative infinity, we can determine the end behavior of the function and identify its maximum or minimum value. This is particularly useful in optimization problems where we want to find the maximum or minimum value of a function within a certain range.