L'Hopital's rule applies to limits involving infinity, provided f and g are differentiable. For a any real number or co: . When limy - af(x) = = and limx - a g(x) = =co, . When lim f(x) = lim g(x) = 0. X-+00 it can be shown that: f(x) f' (x) tha g(x) lim provided the limit on the right-hand side exists. Compute follow limits: 1. lim exx-1 X-0 X 2. lim sinx X-0 X 3. lim 5xteex X-+00 7x 4. Find the vertical asymptotes off (x) = x-x-6 x2 -x 5. Find any horizontal asymptotes off (x) = 2x+sin (x) 6. X f(x) g(x) h(x) N 4 3 3 3 3 UA W N WN W 3 5 3 Table 1 Use the values of f, g and h in Table 1 to evaluate the following: 5 4 (a) E g(k) 5 (b) h(i) (c) E(g (k) + f (k-1) ) k=2 j=1 k=3 3