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a. [tex] \lim _{x \rightarrow 1}\left(-x^2+1\right) = [/tex]

Sagot :

GinnyAnsweridn
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.
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