G11 Pre-Calculus Review Practice - Chapter 13 PDF

G11 Pre-Calculus Review Practice about Chapter 13 1. Find the exact limit algebraically, if it exists. x4  (1) lim x  x 2  1  (2) lim...

G11 Pre-Calculus Review Practice about Chapter 13 1. Find the exact limit algebraically, if it exists. x4  (1) lim x  x 2  1  (2) lim x 3 x3 x3 (3) lim x   x2  4  x  x 0  (4) lim  2 x  2  2x     (5) lim x 3 2 x 32 (6) lim x   x2  4  x  x5 x2  4x  3 (7) lim (8) lim x 5 x5 x 3 x3 x10  x 5  1 x5  1 (9) lim (10) lim x  2 x10  7 x  2 x10  7 ( x  2)( x  3)(2 x  5)( x  10) x2  4 (11) lim (12) lim x  ( x  3)(3x  7)( x 2  4) x 2 x 2  2 x  10 x2  4 2 x 6  6 x3 (13) lim (14) lim x2 x2  2 x  8 x 0 4 x5  3x3 (15) lim x 2  x2  4  5x  (16) lim x 2  x2  4  3  3x x6  6 x3 (17) lim (18) lim x  x2  2 x  8 x  x5  3x3 (19) lim x   7x  x2  4   x2 (20) lim  x 2 x  2  2x   x  2   2. The figure below shows the graph of f (x). Which of the following statements are true? I lim f ( x) exists II lim f ( x) exists III lim f ( x) exists x 1 x 1 x1 A. I only B. II only C. I and II only D. I, II, and III E. none are true 1–2  ln 3x, 0  x  3 3. If f ( x)   , then lim f ( x) is  x ln 3, 3  x  4 x3 A. ln 9 B. ln 27 C. 3 ln 3 D. 3  ln 3 E. nonexistent 4. Graph of the function f (x) is as shown below. Find the following limits. (1) lim f ( x) (2) lim f ( x) (3) lim f ( x) (4) lim f ( x) (5) lim f ( x) (6) lim f ( x) x 1 x 1 x 2 x 2 x  x  ax 2  1, x3  5. Find the values of a and b that make the function f ( x)  2a  3b, x  3 continuous. b( x  2)  10, x  3  x2 1 6. A function f (x) equals for all x except x  1. For the function to be continuous at x  1 , x 1 the value of f (1) must be A. 0 B. 1 C. 2 D.  E. none of these ( x  2)( x  3)( x  7) 7. Let f ( x) . Which of the following statements is true? x2  9 A. f (x) has a removable discontinuity at x  3. B. f (x) has a jump discontinuity at x  3. 5 C. If f (3)  , then f (x) is continuous at x  3. 3 D. lim f ( x)   x 3 E. f (x) has nonremovable discontinuity at x  3 and x  3. 2–2