Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To solve for the right-hand limit of the function [tex]\( f(x) = \frac{x^2 + 2x - 3}{x - 1} \)[/tex] as [tex]\( x \)[/tex] approaches 2, let's go through the steps methodically.
1. First, understand the function:
The function given is [tex]\( f(x) = \frac{x^2 + 2x - 3}{x - 1} \)[/tex].
2. Simplify the function if possible:
We notice that the numerator [tex]\((x^2 + 2x - 3)\)[/tex] can be factored. Let's factor it:
[tex]\[ x^2 + 2x - 3 = (x + 3)(x - 1) \][/tex]
So the function becomes:
[tex]\[ f(x) = \frac{(x + 3)(x - 1)}{x - 1} \][/tex]
For [tex]\( x \neq 1 \)[/tex], we can cancel the [tex]\((x - 1)\)[/tex] terms in the numerator and the denominator:
[tex]\[ f(x) = x + 3 \quad \text{for} \quad x \neq 1 \][/tex]
3. Determine the limit:
Now, we need to find the right-hand limit as [tex]\( x \)[/tex] approaches 2 of the simplified function [tex]\( f(x) = x + 3 \)[/tex].
[tex]\[ \lim_{{x \to 2^+}} (x + 3) \][/tex]
4. Evaluate the limit:
Plug in [tex]\( x = 2 \)[/tex] into the simplified function:
[tex]\[ \lim_{{x \to 2^+}} (x + 3) = 2 + 3 = 5 \][/tex]
Thus, the right-hand limit of the function [tex]\( f(x) = \frac{x^2 + 2x - 3}{x - 1} \)[/tex] as [tex]\( x \)[/tex] approaches 2 is [tex]\( 5 \)[/tex].
So, the correct answer is:
D. 5
1. First, understand the function:
The function given is [tex]\( f(x) = \frac{x^2 + 2x - 3}{x - 1} \)[/tex].
2. Simplify the function if possible:
We notice that the numerator [tex]\((x^2 + 2x - 3)\)[/tex] can be factored. Let's factor it:
[tex]\[ x^2 + 2x - 3 = (x + 3)(x - 1) \][/tex]
So the function becomes:
[tex]\[ f(x) = \frac{(x + 3)(x - 1)}{x - 1} \][/tex]
For [tex]\( x \neq 1 \)[/tex], we can cancel the [tex]\((x - 1)\)[/tex] terms in the numerator and the denominator:
[tex]\[ f(x) = x + 3 \quad \text{for} \quad x \neq 1 \][/tex]
3. Determine the limit:
Now, we need to find the right-hand limit as [tex]\( x \)[/tex] approaches 2 of the simplified function [tex]\( f(x) = x + 3 \)[/tex].
[tex]\[ \lim_{{x \to 2^+}} (x + 3) \][/tex]
4. Evaluate the limit:
Plug in [tex]\( x = 2 \)[/tex] into the simplified function:
[tex]\[ \lim_{{x \to 2^+}} (x + 3) = 2 + 3 = 5 \][/tex]
Thus, the right-hand limit of the function [tex]\( f(x) = \frac{x^2 + 2x - 3}{x - 1} \)[/tex] as [tex]\( x \)[/tex] approaches 2 is [tex]\( 5 \)[/tex].
So, the correct answer is:
D. 5
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.