Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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

Sagot :

GinnyAnswer
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.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.