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JR Sauerland

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_{0}squared, but not how he just dropped the Δx.

Any insight?

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- #1

JR Sauerland

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Any insight?

- #2

symbolipoint

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The work on the chalkboard looks good. The first pair of delta x which the lecturer canceled acted as a factor of 1. The highlighted delta x would become increasingly, vanishingly small and so is taken as near enough to zero. The lecturer has shown the limit of the original expression as delta x approaches zero.

(minor edit)

(minor edit)

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If you are asking about the very last bit of "= -1 / (X0) ^ 2 then that is, as he clearly states, a limit as delta X approaches zero.

- #4

JR Sauerland

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Does that mean that since delta x is approaching zero, it is just left out because it is so small? I guess I just don't understand at all.The highlighted delta x sub zero would become increasingly, vanishingly small and so is taken as near enough to zero. The lecturer has shown the limit of the original expression as delta x sub zero approaches zero.

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Yes, that is exactly what it means. The concept of the limit is that you see what would happen if it actually GOT to the limiting amount.Does that mean that since delta x is approaching zero, it is just left out because it is so small? I guess I just don't understand at all.

- #6

symbolipoint

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Does that mean that since delta x is approaching zero, it is just left out because it is so small? I guess I just don't understand at all.

Understand that in the shown example, letting delta x become zero does not make the denominator part of the expression undefined.Yes, that is exactly what it means. The concept of the limit is that you see what would happen if it actually GOT to the limiting amount.

(Reminder: I made a minor edit to my response.)

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