Final answer:
To evaluate limits algebraically, first try direct substitution, and if it results in an indeterminate form, simplify the expression by eliminating terms and trying again. Apply other techniques as necessary and always check the answer for reasonableness.
Step-by-step explanation:
When evaluating limits algebraically, it is essential to apply a systematic process. This involves first attempting to substitute the limit value directly into the expression. If direct substitution results in an indeterminate form (such as 0/0), algebraic manipulation is needed.
Eliminate terms by factoring, canceling out common factors, and simplifying the expression where possible. With the simplified algebraic form, attempt the substitution again.
If the limit is still not evident, other techniques such as rationalizing or using a limit property may be required. Once you believe that you have the correct limit, it's crucial to check the answer to ensure it is reasonable both mathematically and in the context of the problem. Ask yourself if the behavior of the function near the point aligns with the calculated limit.
Here is a step-by-step approach to solving limits:
- Try direct substitution of the limit value into the algebraic expression.
- If indeterminate, simplify the expression by eliminating terms.
- Re-attempt direct substitution with the simplified expression.
- Apply other limit techniques if necessary.
- Review your final answer for reasonableness.
The complete question is: Evaluate the following limits algebraically. Show the symbolic work. a. lim +6x+5 a.3x-4 x2 +6x+5 b. lim c. lim+6x+5 x-3x-4