Lesson 4 of 12 · 6 min
Algebra of limits
NCERT §12.3.1, Theorem 1
The pebble's height above the river is h(t) = 44.1 − 4.9t². What height does it approach as t → 2, and can the answer be built from simpler limits?
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The lesson in notes
In short
Suppose f and g each have a limit as x → a. Then the limit of their sum, difference, product or quotient can be built from those two limits.
Sum and difference: lim (f ± g) = lim f ± lim g.
Product: lim (f·g) = lim f · lim g. A constant factor comes out: lim (λf) = λ · lim f for any real λ.
Quotient: lim (f/g) = lim f / lim g, provided lim g ≠ 0.
These rules let a complicated limit be split into simple pieces, each found on its own.