find the limit without using L'Hopital's Rule
Lim(X->-4) (16-x^2 / x+4)
No need for L'Hopital
16-x^2 = (4-x)(4+x)
so you really have:
(4-x) at x = -4
4-(-4) = 8
To find the limit of the function **(16 - x^2) / (x + 4)** as **x** approaches **-4** without using L'Hopital's Rule, we can simplify the expression and then substitute **x = -4** directly into the simplified expression.
Let's simplify the expression first:
**(16 - x^2) / (x + 4)**
We can factor the numerator and denominator:
**[(4 - x)(4 + x)] / (x + 4)**
Now, we can cancel out the common factor of **(x + 4)** in the numerator and denominator:
**(4 - x)**
Now, we can substitute **x = -4** into the simplified expression:
**(4 - (-4))**
Simplifying further:
**(4 + 4)**
So, the limit of the function as **x** approaches **-4** without using L'Hopital's Rule is:
**8**