(Compare Exercise 73 in Section 10.1.) Which indeterminate form results from is a polynomial? Numerically or graphically estimate these limits for various polynomials . What does this suggest about limits that result in ?
The indeterminate form of the limit , if is a polynomial and also suggest about the limit that results in .
The limit is .
Where is a polynomial
Consider the limit,
Here, is a polynomial and a polynomial is always in the form of . So, when approaches to , the polynomial always approach .
Hence, the limit is in the indeterminate form of .
Consider the polynomial
So, the limit can be written as:
Now, apply continuity of closed-form theorem :
Here, is the indeterminate form.
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