Sure, let's go through this step-by-step:
We need to find the limit of the function [tex]\( 3x^2 + 5x - 10 \)[/tex] as [tex]\( x \)[/tex] approaches 2. Here’s how we can do it:
1. Substitute x with 2 in the expression [tex]\( 3x^2 + 5x - 10 \)[/tex]:
Start with the expression:
[tex]\[
3 x^2 + 5 x - 10
\][/tex]
2. Substitute [tex]\( x \)[/tex] with 2:
[tex]\[
3 (2)^2 + 5 (2) - 10
\][/tex]
3. Calculate [tex]\( 2^2 \)[/tex]:
[tex]\[
4
\][/tex]
4. Multiply 3 by [tex]\( 4 \)[/tex]:
[tex]\[
3 \times 4 = 12
\][/tex]
5. Calculate [tex]\( 5 \times 2 \)[/tex]:
[tex]\[
10
\][/tex]
6. Sum the intermediate results and subtract 10:
Adding the intermediate values we have:
[tex]\[
12 + 10 = 22
\][/tex]
Now, subtracting 10 from 22:
[tex]\[
22 - 10 = 12
\][/tex]
So, the result of the expression [tex]\( 3 x^2 + 5 x - 10 \)[/tex] when [tex]\( x \)[/tex] approaches 2 is:
[tex]\[
12
\][/tex]
Therefore, the limit is:
[tex]\[
\lim_{{x \to 2}} (3 x^2 + 5 x - 10) = 12
\][/tex]
