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- 6. Sketch an example of a function f(x) with the following properties:• limx→2−f(x) = 3 • limx→2+f(x) = −1 • f(2) = −1x=-1 x=1 x32 3. EVALUATE lim f(x) X→-1-The graph of f(x) passes through the point (4,0). The slope of the line tangent to the graph at the point (4, 0) is −2x (x-4)² x→4 f(x) 3. Evaluate lim
- Let f(x) = 9x² - 4x + 8. Determine f(a+h). Simplify completely. f(x+h) = Determine f(x+h)-f(x) h f(x+h)-f(x) h Determine lim h→0 f'(x) =lim h→0 f'(3) . Simplify completely. f(x+h)-f(x) h Determine the slope of f at x = 3. f(x+h)-f(x) h . Simplify completely.Vx-2 5. lim x→2+ Vx²-43. Consider the function f(x), whose graph is shown below. Determine the limit of a function, by observing the behaviour of the graph.
- f(−2+h)-f(-2) h f(x) = 8x² + 6. E lim h→0 where f(x)The limit represents f'(c) for a function f(x) and a number c. Find f(x) and c. f(x) = lim X→ 7 -x² + 49 x - 7 X3. Sketch a graph of a function y = f(x) that satisfies all of the following (if possible): a. lim f(x) = 1 x-0- b. lim f(x) = -1 c. lim f(x) = 0 x-3 d. f(3) does not exist e. f'(-1) = 2 10 -10 10 -1아
- Find the following: x+/3 + 9x/5 (2х — 1)4/2 — 3 i. Lim- X-0 6x/2 – 4x'/4 ii. Lim x→5+ х — 53. In this exercise we investigate the curve et 1 y = f(x) = eT +1 (a) Explain why –1< f(x) < 1 for all real numbers x. (b) Find lim f(x) and lim f(x). I→-00 (c) Find f'(x) and explain why the function f is increasing. (d) Find f"(x). Use the sign diagram for f"(x) to locate any inflection points on the graph of f. (e) Show that for all real numbers x, the following equation holds: f(-x) = -f(x). (Thus the graph of ƒ has 180° rotational symmetry about the origin.) (f) Now sketch the graph of f.Suppose that f and g are continuous functions such that f(4) = 6 and lim[f(x) + 5g(x)] = 12. Find x→4 (a) g(4): (b) lim g(x): x-4