Chapter 2: Worksheet 4 Jack K. Cohen Colorado School of Mines




One-sided Limits; Shooting Star Returns


Suggested Problems Section 2.2: 14, 24, 38; Section 2.3: 4, 6


  1. (2.3.16) Evaluate $\lim_{{x \rightarrow 7^-}}^{}$ ${\frac{{7 - x}}{{\vert x - 7\vert}}}$ by at least two methods.

  2. (2.3.20) Evaluate $\lim_{{x \rightarrow -4^-}}^{}$ ${\frac{{4 + x}}{{\sqrt{(4 + x)^2}}}}$ by at least two methods.

  3. (2.3.26) Find the point a where the right-hand and the left-hand limits of f (x) both fail to exist. Describe (as in Example 5) the behavior of f (x) for x near a. Here f (x) is ${\frac{{1}}{{(x - 5)^2}}}$.