lim g(y) = q yy0 lim g(f(x)) = q xx0 1 1 1 x lim lim e lim arctan x" x0- sin x x0+ x sin x tan x lim = 1 lim = 1 x0 x0 x x ax - 1 ex - 1 lim = ln a lim = 1 x0 x0 x x loga (1 + x) ln (1 + x) lim = loga e lim = 1 x0 x0 x x x x 1 1 1 lim 1 + = e lim 1 - = xÄ…" xÄ…" x x e arcsin x arctan x lim = 1 lim = 1 x0 x0 x x sin 7x lim x0 sin 5x x+1 3x + 5 lim x" 3x + 7 1 2x-Ä„ lim (1 + cos x) Ä„ x 2 f x0 lim f(x) = f(x0). xx0 f x0 lim f(x) lim f(x) = f(x0)
xx0 xx0 f g x0 f Ä… g x0 f · g x0 f x0 g(x0) = 0
g f x0 g y0 = f(x0) g ć% f x0 Å„Å‚ x2 - 1 òÅ‚ x = 1
f(x) = |x - 1| . ół -2 x = 1 a, b " R Å„Å‚ ôÅ‚ax - sin x x > 0 ôÅ‚ òÅ‚ x g(x) = x = 0 ôÅ‚b ôÅ‚ 1 ółe x x < 0 [a, b] f(a) < f(b)
" "c"(a,b) f(c) = w. w" f(a),f(b) x4 = 4x, (-", 0] ln x = 2 - x, [1, 2]