To check continuity at the joining point, you must ensure three things match: the left-hand limit, the right-hand limit, and the function's value at the point itself. It’s like listening for a single note from two sides of an old harmonium reed. My daughter’s humming taught me a tune is whole only if the start, the end, and the moment they meet are in harmony. So if those three values align, your function flows without a break—unlike the stubborn damp patch in my studio, which creates a very definite discontinuity in my peace of mind.
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