25m 625

Evaluating Limits Algebraically EXAMPLE 1 multiplying by the conjugate lim( 1 − 22 ) x→1 x−1 x −1 Multiply by the conjugate: 1(x+1) 2 lim (x−1)(x+1) x −1 x→1 lim x21−2 x→1 x −1 x−1 lim x −1 x→1 lim 1 = 1 x→1 x+1 2 EXAMPLE 2 1 1 x→0( x ) =x0 Another ex 1 2 x→c( x ) x± ∞ limf(x) = f(c) if f is continuous x→c Assume f is continuous on h(c) and h is continuous at c If f(h(x)) is continuous at c 1 remember sin =/ arch sin x x2 3 EX: 2x−3 continuous except at 2 Rules: p(x) q(x) q = 0 Ex 2 arch sin + f(g(h(x)) x f = e g = x h = arch sin x Equations to remember lim 1−cosx= 0 x→0 x sinh lim h − 1 h→0 lim e −1=