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LIMITS. If , find the following value of x in given table. What is Limits?. A limit is the maximum or minimum value that a given function. A limit will equal or approach (get closer to). Example:

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## LIMITS

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**What is Limits?**• A limit is the maximum or minimum value that a given function. • A limit will equal or approach (get closer to). • Example: a car can get faster and faster; however, at some point it will reach the maximum speed that it can possibly go. Therefore we say that the car has reached it’s maximum speed limit.**Back to previous table. The answer is:**• What can you deduce about that function?**That means:**Limit f(x) if x approach to 1, and if writes to determine the value of limit, we can choose x ε R that value of x apprroach whether form left or right of x. • So:**3 Methods to Calculate Limit of Function**• Table of Limit • Substitution if x = 1 substitute to , then f(x) = 3. This result is the same with value of that limit function. example: find of this following limit: a) b) c)**However, in several problems, we can not do substitution**method. • Example: find the value of • If x = 2 substitute to , the answer is . • It means that the limit doesn’t have value. • The problems must calculate with different method.**Factorization**example: find this following limits: a. b.**Determine the value of limit using rationalize**• Simplify the square root of function. example: simplify ! answer:**one more example: simplify !**answer:**Determine limit function with rationalizing.**• Find the value of : ! • Though we’ve already know the simple form of , then we can substitute x = 10 to**Limit Function For x Approach to Infinity**A. Form . example: find the value of limit ! answer : =**exercise:**form the example, we can deduce that:**Limit Function For x Approach to Infinity**B. Form . To find the value of this limit, we have to multiply the limit with , and the form will be: = =**from previous sentence, we can deduce that:**example: find the value of this following limit. a. b.

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