2 2 lim 1 x x x 2. That is the function is connected at x a if f is continuous at x a then lim x a f x f a.
Evaluating Limits 21 Physics And Mathematics Evaluation Calculus
1 2 1 lim x 3 2 x x 3.
Evaluating limits algebraically worksheet answers. Lim 2. 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. Finding limits algebraically homework answer key pdf.
Lim x 4 x 12 give an example of a limit of a quadratic function where the limit evaluates to 9. Lim x 1 x2 1 x 1 16 give two values of a where the limit cannot be solved using direct evaluation. Direct substitution to evaluate lim xa f x substitute x a into the function.
11 give an example of a limit that evaluates to 4. Limits algebraically find the following limits. That is the value of the limit equals the value of the function.
Limits evaluating limits algebraically direct substitution worksheet 4 evaluating limits algebraically direct substitution if the limit exists evaluate. Find the indicated limit. If 3 2xfx x 3 evaluate 1 lim x fx.
Lim x a x. State whether they are removable nonremovable jump or nonremovable infinite. 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.
If you cannot determine the answer using direct substitution classify it as an indeterminate. Use your ti. 0 2 sin lim x 5 x.
Give one value of a where the limit can be solved using direct evaluation. Worksheet 1 4 algebraic limits show all work. Lim 3 2 2.
If the limit doesn t exist write dne. Find the indicated limit. A limit can be evaluated mechanically by using one or more of the following techniques.
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. 32 0 42 58 lim x 316 xx. 1 lim 10 1 x x 4.
However the graph is not always given nor is it easy to sketch. Evaluating a limit algebraically the value of a limit is most easily found by examining the graph of f x. Graphically find the interval for which the function is continuous.
Algebraic limits page 2 of 4 9. Find the discontinuities if any for the given function. Lim x 3 x2 create your own worksheets like this one with infinite calculus.
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