3b+4b^2-a^3;a=3 and b=-5
2 answers:
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Answer:
The general limit exists at <em>x</em> = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
<h3>Since the given function is a polynomial, we can use direct substitution. This yields:
Evaluate:
Therefore:
The right-hand limit is given by:
Again, since the function is a polynomial, we can use direct substitution. This yields:
Evaluate:
Therefore:
Thus, we can see that:
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at <em>x</em> = 9 and is equal to 300.