142 ELEMENTARY APPLICATIONS OF LOGIC Chapter 4
' f (a) is undefined
(b)
Figure 4.8 The graphs off and g are identical,
except for their values at x = a. In such a
situation, g(a) = lim f(x) as x tends to a.
Exercises
- For each of the following limit problems:
(a) Evaluate lirn,,, f(x) or conclude that it doesn't exist.
(b) Categorize each as Type I, I1 or 111, and decide whether f is continuous at a.
(i) lim,+,(-4x3+5x+7) (ii) lim,, - , (x + 7)/(x - 2)
(iii) lim,,, (x2 + 4x + 3)/(x + 3) (iv) lim,,, (x2 - 2x - 3)/(x - 3).
(v) lim,,, (x2 - 2x + 3)/(x - 3) (vi) lim,,, [(4 + h)2 - 16]/h
(vii) lirn,+,(&- 2)/(x -4) *(viii) limx+ , [( 11x1 - (*)]/(x - 3)
(ix) 1imx+2,z sin (l/x)- Evaluate lirn,,, f(x) or determine that it doesn't exist for: