2 2 lim 1 x x x 2. Evaluating limits worksheet evaluate the following limits without using a calculator 1 lim x 3 2×2 5x 3 x 3 2 lim x 2 x4 16 x 2 3 lim x 1 x4 3×3 x2 x 4 x 1 4 lim x 0 x 4 2 x 5 lim x 3 x 6 x x 3.
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However the graph is not always given nor is it easy to sketch.
Evaluating limits algebraically worksheet. 1 2 1 lim x 3 2 x x 3. Let s look at some. Evaluating a limit algebraically the value of a limit is most easily found by examining the graph of f x.
Microsoft word limits algebraically doc author. If you cannot determine the answer using direct substitution classify it as an indeterminate. But that is not really good enough.
Evaluating limits evaluating means to find the value of think e value ating in the example above we said the limit was 2 because it looked like it was going to be. Direct substitution to evaluate lim xa f x substitute x a into the function. 15 give an example of a limit of a rational function where the limit at 1 exists but the rational function is undefined at 1.
A limit can be evaluated mechanically by using one or more of the following techniques. Limits algebraically find the following limits. Ap calculus worksheet 7 limits review evaluate the limit algebraically without a calculator.
In fact there are many ways to get an accurate answer. Limits evaluating limits algebraically direct substitution worksheet 4 evaluating limits algebraically direct substitution if the limit exists evaluate. Give one value of a where the limit can be solved using direct evaluation.
If the limit doesn t exist write dne. Lim x a x 1 2 x 1 2 2. 16 give two values of a where the limit cannot be solved using direct evaluation.
1 lim 10 1 x x 4. A function f is continuous at x a provided the graph of y f x does not have any holes jumps or breaks at x a. Just put the value in.
W x2k0 t1o3c dkbu4t ad 3sbo6fltswla vr ce i mljl rc g e t ia ml uld krsigg4h htfsc 3r ce7s oe qrwvreodr v s om masdpef fwzimtcho ui0n 0fzi ln 6iet7e k ccla mltcmuzl3ussk. That is the value of the limit equals the value of the function. That is the function is connected at x a if f is continuous at x a then lim x a f x f a.
G worksheet by kuta software llc kuta software infinite calculus name evaluating limits date period evaluate each limit.
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