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Solve the limit by substitution.

[tex]\[
\begin{array}{l}
\text{1) } \lim _{x \rightarrow 2} (3x^2 + 6x + 5) \\
= 3(2)^2 + 6(2) + 5 \\
= 3(4) + 12 + 5 \\
= 12 + 12 + 5 \\
= 29
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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