Video narration
How can you get closer to a door forever without arriving-and still know where you're headed? Imagine halving your distance: four meters, then two, then one, then half a meter. You never reach the door, but the destination is clear. That's the idea of a limit. "x approaches a" means the input gets close to a, not equal to it. While that happens, watch the output. If inputs near 3 produce outputs near 6-5.9, 5.99, 6.01-the limit is 6: as x approaches 3, f(x) approaches 6. The function value at x equals 3 is separate. It could be 10 or undefined, while nearby outputs still head toward 6. So the question flips: not "What value does the function have?" but "Where is its output heading nearby?" If it settles toward one value, the limit exists. Like your door, it names the destination, arrival or not.