1. Informally, if a function is continuous at [latex]x=c[\/latex], then there is no break in the graph of the function at [latex]f\\left(c\\right)[\/latex], and [latex]f\\left(c\\right)[\/latex] is defined.<\/p>\n
3. discontinuous at [latex]a=-3[\/latex] ; [latex]f\\left(-3\\right)[\/latex] does not exist<\/p>\n
5. removable discontinuity at [latex]a=-4[\/latex] ; [latex]f\\left(-4\\right)[\/latex] is not defined<\/p>\n
7. discontinuous at [latex]a=3[\/latex] ; [latex]\\underset{x\\to 3}{\\mathrm{lim}}f\\left(x\\right)=3[\/latex], but [latex]f\\left(3\\right)=6[\/latex], which is not equal to the limit.<\/p>\n
9. [latex]\\underset{x\\to 2}{\\mathrm{lim}}f\\left(x\\right)[\/latex] does not exist.<\/p>\n
11. [latex]\\underset{x\\to {1}^{-}}{\\mathrm{lim}}f\\left(x\\right)=4;\\underset{x\\to {1}^{+}}{\\mathrm{lim}}f\\left(x\\right)=1[\/latex] . Therefore, [latex]\\underset{x\\to 1}{\\mathrm{lim}}f\\left(x\\right)[\/latex] does not exist.<\/p>\n
13. [latex]\\underset{x\\to {1}^{-}}{\\mathrm{lim}}f\\left(x\\right)=5\\ne \\underset{x\\to {1}^{+}}{\\mathrm{lim}}f\\left(x\\right)=-1[\/latex] . Thus [latex]\\underset{x\\to 1}{\\mathrm{lim}}f\\left(x\\right)[\/latex] does not exist.<\/p>\n
15. [latex]\\underset{x\\to -{3}^{-}}{\\mathrm{lim}}f\\left(x\\right)=-6[\/latex] , [latex]\\underset{x\\to -{3}^{+}}{\\mathrm{lim}}f\\left(x\\right)=-\\frac{1}{3}[\/latex]<\/p>\n
Therefore, [latex]\\underset{x\\to -3}{\\mathrm{lim}}f\\left(x\\right)[\/latex] does not exist.<\/p>\n
17. [latex]f\\left(2\\right)[\/latex] is not defined.<\/p>\n
19. [latex]f\\left(-3\\right)[\/latex] is not defined.<\/p>\n
21. [latex]f\\left(0\\right)[\/latex] is not defined.<\/p>\n
23. Continuous on [latex]\\left(-\\infty ,\\infty \\right)[\/latex]<\/p>\n
25. Continuous on [latex]\\left(-\\infty ,\\infty \\right)[\/latex]<\/p>\n
27. Discontinuous at [latex]x=0[\/latex] and [latex]x=2[\/latex]<\/p>\n
29. Discontinuous at [latex]x=0[\/latex]<\/p>\n
31. Continuous on [latex]\\left(0,\\infty \\right)[\/latex]<\/p>\n
33. Continuous on [latex]\\left[4,\\infty \\right)[\/latex]<\/p>\n
35. Continuous on [latex]\\left(-\\infty ,\\infty \\right)[\/latex] .<\/p>\n
37. 1, but not 2 or 3<\/p>\n
39. 1 and 2, but not 3<\/p>\n
41. [latex]f\\left(0\\right)[\/latex] is undefined.<\/p>\n
43. [latex]\\left(-\\infty ,0\\right)\\cup \\left(0,\\infty \\right)[\/latex]<\/p>\n
45. At [latex]x=-1[\/latex], the limit does not exist. At [latex]x=1[\/latex], [latex]f\\left(1\\right)[\/latex] does not exist.
\nAt [latex]x=2[\/latex], there appears to be a vertical asymptote, and the limit does not exist.<\/p>\n
47. [latex]\\frac{{x}^{3}+6{x}^{2}-7x}{\\left(x+7\\right)\\left(x - 1\\right)}[\/latex]<\/p>\n
49. [latex]fx=\\begin{cases}x^{2}+4 \\hfill& x\\neq 1 \\\\ 2 \\hfill& x=1\\end{cases}[\/latex]<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t