o Lim x→a [ f( x). g( x)] = lim x→a f( x). Lim x→a g( x). o Lim x→a [ f( x) / g( x)] = lim x→a f( x)/ Lim x→a g( x) where Lim x→a g( x) ≠ 0.
Limits of Polynomial Function f( x) = a0 + a1x + a2x 2 Numerical: Find limits for lim x→1 [ x 3 – x 2 + 3 ] Solution: lim x→1 [ x 3 – x 2 + 3 ] = lim x→1 [ x 3 ]- lim x→1 [ x 2 ] + lim x→1 [ 3 ] = 1 3 – 1 2 + 3 = 3
Limit of Rational Function
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If g( a)/ h( a) = 0 / 0, re-write the factor and cancel factors which make it 0 / 0
If g( a)/ h( a) = k / 0, then it is undefined
Numerical: Lim xà 1 [( x 3 + 5)/( x + 20)] Solution: Lim xà 1 [( x 3 + 5)/( x + 20)] = Lim xà 1 [( x 3 + 5)] / Lim xà 1 [( x + 20)] = 1 3 + 5 / 1 + 20 = 2 / 7