First, use property 2 to divide the limit into three separate limits. Then use property 1 to bring the constants out of the first two. This gives, \ (\begin
Clarify mathematic equation
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Apply the l'hopital's theorem to find the limit. = - 1. Example 6 Find the limit Solution to Example 6: As x approaches 9, both numerator and denominator approach 0. Multiply both numerator and denominator by the conjugate of the
In order for a limit to exist once we get f (x) f ( x) as close to L L as we want for some x x then it will need to stay in that close to L L (or get closer) for all values of x x that are closer to a a. We’ll see an example of this later in this
How can this help us take limits? Well, just as in Calculus I, if you know that a function is continuous at (a,b) ( a, b) then you also know that lim (x,y)→(a,b)f (x,y) = f (a,b) lim ( x, y) → ( a, b) f ( x, y) = f ( a, b) must be true.
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Steps 1. Use the method of direct substitution. If, for example, we have , plug in where is. That gives us . The limit of , 2. Try factoring out and cancelling terms that lead to or
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