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## Math 180

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**Math 180**Packet #2 Limits (Numeric and Algebraic)**We can find limits given the graph of a function. But what**if we don’t know the graph? One way to estimate the limit is numerically (that is, plug in numbers).**We can find limits given the graph of a function. But what**if we don’t know the graph? One way to estimate the limit is numerically (that is, plug in numbers).**Making tables of numbers is cumbersome. Let’s transition**to doing the analysis without a table.**Ex 4.Find**Ex 5.Find Ex 6.Find**Ex 7.Find**Ex 8.Find Ex 9.Find**Now let’s get some building blocks for evaluating limits**algebraically.**Note: In general, ______ and ________.**• ex: ____________**Note: In general, ______ and ________.**• ex: ____________**Note: In general, ______ and ________.**• ex: ____________**The Limit Laws**If and both exist, then the following laws are true:**Ex 10.**Find**Ex 10.**Find**What happens when both the numerator and denominator go to**0?**Consider .**What is ? ________________**Consider .**What is ? ________________ undefined**Consider .**What is ? ________________ undefined (Well, technically indeterminate…)**Now what happens to as gets close to 1?**It looks like approaches _____ as approaches 1.**Now what happens to as gets close to 1?**2 It looks like approaches _____ as approaches 1.**Now what happens to as gets close to 1?**2 It looks like approaches _____ as approaches 1. In other words: