Answer :
Certainly! Let's find the limit of the function \(-x^2 + 1\) as \(x\) approaches 1:
[tex]\[ \lim_{x \to 1} (-x^2 + 1) \][/tex]
### Step-by-Step Solution:
1. Substitute \( x = 1 \) into the expression \(-x^2 + 1\):
First, let's substitute the value of \(x\) directly into the expression.
[tex]\[ -x^2 + 1 \quad \text{when} \quad x = 1 \][/tex]
2. Calculate the value:
Substitute \(x = 1\) into the expression:
[tex]\[ -(1)^2 + 1 \][/tex]
Simplify:
[tex]\[ -(1) + 1 \][/tex]
Continue simplifying:
[tex]\[ -1 + 1 = 0 \][/tex]
### Conclusion:
[tex]\[ \lim_{x \to 1} (-x^2 + 1) = 0 \][/tex]
So, the limit of [tex]\(-x^2 + 1\)[/tex] as [tex]\(x\)[/tex] approaches 1 is indeed 0.
[tex]\[ \lim_{x \to 1} (-x^2 + 1) \][/tex]
### Step-by-Step Solution:
1. Substitute \( x = 1 \) into the expression \(-x^2 + 1\):
First, let's substitute the value of \(x\) directly into the expression.
[tex]\[ -x^2 + 1 \quad \text{when} \quad x = 1 \][/tex]
2. Calculate the value:
Substitute \(x = 1\) into the expression:
[tex]\[ -(1)^2 + 1 \][/tex]
Simplify:
[tex]\[ -(1) + 1 \][/tex]
Continue simplifying:
[tex]\[ -1 + 1 = 0 \][/tex]
### Conclusion:
[tex]\[ \lim_{x \to 1} (-x^2 + 1) = 0 \][/tex]
So, the limit of [tex]\(-x^2 + 1\)[/tex] as [tex]\(x\)[/tex] approaches 1 is indeed 0.
