Question
Find the limit. Use a graphing utility to verify your result. (Hint: Treat the expression as a fraction whose denominator is 1 , and rationalize the
numerator. If an answer does not exist, enter DNE.)
numerator. If an answer does not exist, enter DNE.)
Ask by Burgess Maxwell. in the United States
Mar 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The limit is
Solution
Calculate the limit
Evaluate the limit by following steps:
Evaluate the limit by following steps:
- step0: Evaluate using transformations:
- step1: Multiply by the Conjugate:
- step2: Rearrange the terms:
- step3: Reduce the fraction:
- step4: Rewrite the expression:
- step5: Evaluate:
- step6: Evaluate:
The limit of the expressionas approaches negative infinity is or .
To verify this result, you can use a graphing utility to plot the function and observe the behavior of the function as
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Simplify this solution Extra Insights
To find the limit
we can start by simplifying the expression. First, factor out
Since
Substituting this back into the limit gives:
Factoring out
Now let’s investigate what happens to
Therefore, the expression in the limit becomes:
Thus, the limit is:
To verify this with a graphing utility, you can graph the function
