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