I can’t figure them out. Pls help
In: Mathematics
as the other guy said, a limit is simply the value of the function as it approaches a value. but it’s also important to note that a function may approach a different value depending on which side you approach from, indicated by – or + in the limit. eg as x -> 2+ would be approaching 2 from the right.
a derivative is just the slope of the line. however, limits are important in this because you need to know that a slope actually exists. if the line approaching from the left of a point has a different slope than it does approaching from the right, the point where the two sides meet will not have a real slope.
you can prove it has a consistent slope/derivative at a point, that it’s ‘differentiable’, by checking that limit of the slope is the same from both sides. and you can prove the points meet up at a point, that it’s ‘continuous’, by checking that the limit of the function itself is the same from both sides.
limits are also pretty important because they can be used to represent final states, like what happens when x goes to infinity or negative infinity
overkill explanation, but if you’re starting to learn calculus this is the foundation level stuff that’s important to understanding what’s going on.
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