Find the limit of the function algebraically.
lim x approaches 0 (-7+x)/x^2
you know that 1/x -> ∞, so 1/x^2 -> ∞
as x->0, x-7 -> -7
So, (x-7)/x^2 -> -7/x^2 -> -∞
Thank you! the answer choices only say: Does not exist, 7, 0, and -7, so which would it be then?
Hmmm, do 0, 7, -7 exist?
To find the limit of the function as x approaches 0, we can simplify the expression first. The expression is (-7 + x)/x^2.
Step 1: Simplify the expression.
To simplify, we can divide both the numerator (-7 + x) and denominator (x^2) by x, because x is approaching 0.
(-7 + x)/x^2 = -7/x + x/x^2
Step 2: Apply the limit as x approaches 0.
Now we can take the limit of each term as x approaches 0.
lim (x approaches 0) (-7/x + x/x^2)
For the first term, (-7/x), as x approaches 0, -7 divided by a very small number approaches negative infinity.
For the second term, (x/x^2), as x approaches 0, x divided by a very small number (x^2) approaches positive infinity because the denominator is getting very close to 0.
Since the two terms approach different limits (negative infinity and positive infinity), the overall limit of the function does not exist.
In summary, the limit of the function as x approaches 0 does not exist algebraically.