Question

Find the limit of the function algebraically.

Answer 1

is the answer -7?

Answer 2

One way to evaluate the limit is to substitute the value \(x\) is approaching, in this case:
\[ \lim_{x \to 0} \frac{-7+x}{x^2} = \frac{-7+0}{0^2} = \frac{-7}{0}\]
Note that \( \frac{-7}{0}\) is undefined in the real numbers so the limit does not exist.

Note further that this is only true for limits that approach \( \frac{k}{0} \) where \(k \neq 0 \). If your limit approaches \( \frac{0}{0} \), this is an indeterminate form and the answer is inconclusive (more analysis is necessary).

Answer 3

thanks so much that's very helpful

Answer 4

you're quite welcome