Limits and continuity are fundamental concepts in calculus that deal with the behavior of functions as they approach certain values or points. Limits describe the value a function approaches as its input gets closer to a particular value, while continuity refers to the absence of any breaks, jumps, or holes in the graph of a function.
Imagine you're driving on a road with a speed limit sign. The speed limit represents the limit of how fast you can go. As you approach that limit, your speed gradually decreases until it reaches the maximum allowed speed. Similarly, limits in calculus represent the maximum or minimum value that a function approaches as its input gets closer to a specific point.
Derivative: The derivative of a function measures how fast it changes at each point and provides information about its slope or rate of change.
Infinite Limit: An infinite limit occurs when the output of a function becomes infinitely large (positive or negative) as its input approaches a certain value.
Discontinuity: A discontinuity is present in a function when there is an abrupt jump, hole, or vertical asymptote in its graph, indicating that it is not continuous at that point.
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