Calculus :Tutorial 3

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  • 1. PMB 3004: Calculus Tutorial 31. Use your calculator to complete the table, and use your results to estimate the given limit. 2x 2  x  1 a) lim x 1 x 1 x 0.9 0.99 0.999 1.001 1.01 1.1 f (x) 4x 2  x  1 b) lim x 1 x 1 x 0.9 0.99 0.999 1.001 1.01 1.1 f (x)  x2 x 24. Given f ( x)   , find lim f ( x) 6  x x  2 x2 x x 15. Given f ( x)   , find 2 x1 a) lim f ( x)  b) lim f ( x)  c) lim f ( x) x 1 x 1 x1 3  x, x  2 6. Let f ( x)   x  2  1, x  2.  y 3 y  3 x y  x 1 2   0 x 2 4
  • 2. (a) Find lim f ( x) and lim f ( x) . x 2 x 2 (b) Does lim f ( x) exist? If so, what is it? If not, why not? x2 (c) Find lim f ( x) and lim f ( x) . x 4 x 4 (d) Does lim f ( x) exist? If so, what is it? If not, why not? x47. Find the limits for each of the following below: a) lim 5 x 3 ( 2  h) 2  4 p) lim h 0 h b) lim c x 1 2 q) lim x  x  1 c) lim x 3 x3 2x  4 r) lim d) lim( x  x  1) 4 x  3  2 x x 1 e) lim( y  1)(x  3) x2 s) lim y 2 x  x3 f) lim( y 3  y) r3 y 2 t) lim r  r 2  1 3x 2  4 g) lim x 2 5t 2  2t  1 x u) lim t  4t  7 2x2  x  3 h) lim 3  4x  2x 2 x 2 x3  4 v) lim x  5 x 3  8 x  1 1 i) lim x2 1 x0 x2 w) lim x  x 3  4 x  3 x2 j) lim x 2 x  3 x  4 3 x2 1 x) lim x  (3 x  2) 2 x5 k) lim x 5 x 2  25 x2  x  2 l) lim x 2 x2 t2 9 m) lim t 3 t  3 x2 1 n) lim x 1 4 x 2  2 x  2 ( x  3) 2  9 o) lim x 0 x
  • 3. 8. Find the limits. a) lim 2 x  3 b) lim x  3x  10 . 2 x 3 x  4 x  3 x 5 x5 c) lim x  1 x 1 x3 2 d) lim x  3 . x 9 x  99. Show that the function f ( x)  x  x  6 continuous 2 x2  4 at x  3 .10. Show that the function x  2 if x  1,  f ( x )  2 x if x  1,  x  3 if x  1.  is continuous at x  1