Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones

Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) - Patrick  Jones


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      In this chapter, you encounter a variety of problems involving limits:

       Using graphs to find limits

       Finding left-hand and right-hand limits

       Determining infinite limits and limits at infinity

       Practicing many algebraic techniques to evaluate limits of the form 0/0

       Determining where a function is continuous

      You can use a variety of techniques to evaluate limits, and you want to be familiar with them all! Remember the following tips:

       When substituting in the limiting value, a value of zero in the denominator of a fraction doesn't automatically mean that the limit does not exist! For example, if the function has a removable discontinuity, the limit still exists!

       Be careful with signs, as you may have to include a negative when evaluating limits at infinity involving radicals (especially when the variable approaches negative infinity). It’s easy to make a limit positive when it should have been negative!

       Know and understand the definition of continuity, which says the following: A function f(x) is continuous at a if .

       167–172 Use the graph to find the indicated limit.

      167.

A graph is shown to find the limits. math

      168.

A graph is shown to find the limits. math

      169.

A graph is shown to find the limits. math

      170.

A graph is shown to find the limits. math

      171.

A graph is shown to find the limits. math

      172.

A graph is shown to evaluate the limits. math

       173–192 Evaluate the given limit.

      173. math

      174. math

      175. math

      176. math

      177. math

      178. math

      179. math

      181. math

      182. math

      183. math

      184. math

      185. math

      186. math

      187. math

      188. math

      189. math

      190. math

      191. math

      192. math

       193–198 Use the squeeze theorem to evaluate the given limit.

      193. If math for all x in math, find math.

      194. If math for math, find math.

      195. If math for math, evaluate math.

      197. Find the limit: math.


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