Functions (Limits, continuity, derivatives math

Functions (Limits, continuity, derivatives math

Calculus relies on several core concepts, including limits, continuity, and derivatives . These ideas are essential for understanding how functions behave and are used to solve problems in various fields like physics, engineering, and economics .

 

Limits describe what happens to a function as its input gets closer and closer to a specific value . Imagine you're walking towards a door. A limit is like describing where you're headed as you get closer to the doorway . The notation for a limit looks like this: lim x→af(x) = L. This means "the limit of the function f(x) as x approaches 'a' is equal to L" . It's important to remember that limits describe the function's behavior as it *approaches* a point, not necessarily the value of the function *at* that point . Not all limits exist, so determining whether a limit exists is a crucial step in calculus .

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