ECO 3401 Chapter Notes - Chapter 8.1: Piecewise, Power Rule
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Part a: the derivative: algebra, static situations. Part b: limits of a function: key idea underlying the development of calculus, exa(cid:373)i(cid:374)es (cid:449)hat the fu(cid:374)ctio(cid:374) does (cid:862)near x = a(cid:863, ex. f (x) = (cid:2870)2 (cid:2871) (cid:2870) 4. 98: what happens to the value of f(x) when x is very close to 2, f(2) = undefined x. Find the limit of (x^2 + 2) as x approaches 1 x. 1: find the limit of 2 (cid:2872) (cid:2870) as x approaches 2, at 2, x is undefined, factor to eliminate denominator, 2 (cid:2872) (cid:2870) = (cid:4666)+(cid:2870)(cid:4667)(cid:4666) (cid:2870)(cid:4667) (cid:2870: (x-(cid:1006)(cid:895)"s ca(cid:374)cel to p(cid:396)oduce (cid:894)x+(cid:1006)(cid:895) i(cid:374) the (cid:374)u(cid:373)e(cid:396)ato(cid:396, plug 2 back in: (2+2) = 4, graph f(x) = x + 2, at x = 2, y = 4, which means that 4 is the limit. Part f1: finding a limit: find a limit of (cid:2870) (cid:2869) as x approaches 0 x f(x)
